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We determine a previously unknown universal quantity, the location of the Yang-Lee edge singularity for the $\mathrm{O}(N)$ theories in a wide range of $N$ and various dimensions. At large $N$, we reproduce the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ analytical result on the location of the singularity and, additionally, we obtain the mean-field result for the location in $d=4$ dimensions. In order to capture the nonperturbative physics for arbitrary $N$, $d$ and complex-valued external fields, we use the functional renormalization group approach.

Driven periodic elastic systems such as charge-density waves (CDWs) pinned by impurities show a nontrivial, glassy dynamical critical behavior. Their proper theoretical description requires the functional renormalization group. We show that their critical behavior close to the depinning transition is related to a much simpler model, $O(n)$ symmetric ${\ensuremath{\phi}}^{4}$ theory in the unusual limit of $n\ensuremath{\rightarrow}\ensuremath{-}2$. We demonstrate that both theories yield identical results to four-loop order and give both a perturbative and a nonperturbative proof of their equivalence. As we show, both theories can be used to describe loop-erased random walks (LERWs), the trace of a random walk where loops are erased as soon as they are formed. Remarkably, two famous models of non-self-intersecting random walks, self-avoiding walks and LERWs, can both be mapped onto ${\ensuremath{\phi}}^{4}$ theory, taken with formally $n=0$ and $n\ensuremath{\rightarrow}\ensuremath{-}2$ components. This mapping allows us to compute the dynamic critical exponent of CDWs at the depinning transition and the fractal dimension of LERWs in $d=3$ with unprecedented accuracy, $z(d=3)=1.6243\ifmmode\pm\else\textpm\fi{}0.001$, in excellent agreement with the estimate $z=1.62400\ifmmode\pm\else\textpm\fi{}0.00005$ of numerical simulations.

We use the functional renormalization group method to study a three-orbital model for superconducting ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$. Although the pairing symmetry is found to be a chiral $p$ wave, the atomic spin-orbit coupling induces near nodes for quasiparticle excitations. Our theory explains a major experimental puzzle between a $d$-wavelike feature observed in thermal experiments and the chiral $p$-wave triplet pairing revealed in nuclear-magnetic resonance and the Kerr effect.

We study the quantum sine-Gordon model within a nonperturbative functional renormalization-group approach (FRG). This approach is benchmarked by comparing our findings for the soliton and lightest breather (soliton-antisoliton bound state) masses to exact results. We then examine the validity of the Lukyanov-Zamolodchikov conjecture for the expectation value $\langle e^{\frac{i}{2}n\beta\varphi}\rangle$ of the exponential fields in the massive phase ($n$ is integer and $2\pi/\beta$ denotes the periodicity of the potential in the sine-Gordon model). We find that the minimum of the relative and absolute disagreements between the FRG results and the conjecture is smaller than 0.01., Comment: 5+5 pages, 8 figures

Tricriticality, as a sister of criticality, is a fundamental and absorbing issue in condensed matter physics. It has been verified that the bosonic Wilson-Fisher universality class can be changed by gapless fermionic modes at criticality. However, the counterpart phenomena at tricriticality have rarely been explored. In this paper, we study a model in which a tricritical Ising model is coupled to massless Dirac fermions. We find that the massless Dirac fermions result in the emergence of a new tricritical point, which we refer to as the chiral tricritical point (CTP), at the phase boundary between the Dirac semimetal and the charge-density-wave insulator. From functional renormalization group analysis of the effective action, we obtain the critical behaviors of the CTP, which are qualitatively distinct from both the tricritical Ising universality and the chiral Ising universality. We further extend the calculations of the chiral tricritical behaviors of Ising spins to the case of Heisenberg spins. The experimental relevance of the CTP in two-dimensional Dirac semimetals is also discussed., Comment: 4.3 pages + supplemental material, 2 figures, published version

Motivated by the recent synthesis of the spin-1 A-site spinel NiRh$_{\text 2}$O$_{\text 4}$, we investigate the classical to quantum crossover of a frustrated $J_1$-$J_2$ Heisenberg model on the diamond lattice upon varying the spin length $S$. Applying a recently developed pseudospin functional renormalization group (pf-FRG) approach for arbitrary spin-$S$ magnets, we find that systems with $S \geq 3/2$ reside in the classical regime where the low-temperature physics is dominated by the formation of coplanar spirals and a thermal (order-by-disorder) transition. For smaller local moments $S$=1 or $S$=1/2 we find that the system evades a thermal ordering transition and forms a quantum spiral spin liquid where the fluctuations are restricted to characteristic momentum-space surfaces. For the tetragonal phase of NiRh$_{\text 2}$O$_{\text 4}$, a modified $J_1$-$J_2^-$-$J_2^\perp$ exchange model is found to favor a conventionally ordered N\'eel state (for arbitrary spin $S$) even in the presence of a strong local single-ion spin anisotropy and it requires additional sources of frustration to explain the experimentally observed absence of a thermal ordering transition., Comment: 11 pages, 14 figures

Antiferromagnetic Heisenberg model on the triangular lattice is perhaps the best known example of frustrated magnets, but it orders at low temperatures. Recent density matrix renormalization group (DMRG) calculations find that next nearest neighbor interaction $J_2$ enhances the frustration and leads to a spin liquid for $J_2/J_1\in (0.08,0.15)$. In addition, DMRG study of a dipolar Heisenberg model with longer range interactions gives evidence for a spin liquid at small dipole titling angle $\theta\in[0,10^\circ)$. In both cases, the putative spin liquid region appears to be small. Here, we show that for the triangular lattice dipolar Heisenberg model, a robust quantum paramagnetic phase exists in a surprisingly wide region, $\theta\in [0,54^\circ)$, for dipoles tilted along the lattice diagonal direction. We obtain the phase diagram of the model by functional renormalization group (RG) which treats all magnetic instabilities on equal footing. The quantum paramagnetic phase is characterized by a smooth continuous flow of vertex functions and spin susceptibility down to the lowest RG scale, in contrast to the apparent breakdown of RG flow in phases with stripe or spiral order. Our finding points to a promising direction to search for quantum spin liquids in ultracold dipolar molecules., Comment: 5 pages, 2 figures and the supplementary materials

We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to deform a 2D tensor network into small loops and then optimize the tensors on each loop. In this way, we remove short-range entanglement at each iteration step and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model., Comment: 15 pages, 11 figures, accepted version for Phys. Rev. Lett

We develop and apply the Diagrammatic Monte Carlo technique to address the problem of stability of the Dirac liquid state (in a graphene type system) against strong long-range part of the Coulomb interaction. So far, all attempts to deal with this problem in the field-theoretical framework were limited either to perturbative or RPA treatments, with diametrically opposite conclusions. Our calculations aim at the approximations-free solution with controlled accuracy by computing vertex corrections from higher-order skeleton diagrams and establishing the renormalization group flow of the effective Coulomb coupling constant. We unambiguously show that with increasing the system size $L$ (up to $ln(L) \sim 40$), the coupling constant always flows towards zero; i.e. the two dimensional Dirac liquid is an asymptotically free $T=0$ state with divergent Fermi velocity., Comment: 5 pages, 4 figures

We establish a precise connection between discrete wavelet transforms (WTs) and entanglement renormalization (ER), a real-space renormalization group transformation for quantum systems on the lattice, in the context of free particle systems. Specifically, we employ Daubechies wavelets to build approximations to the ground state of the critical Ising model, then demonstrate that these states correspond to instances of the multi-scale entanglement renormalization ansatz (MERA), producing the first known analytic MERA for critical systems., Comment: Main text: 5 pages, 2 figures. Appendices: 5 pages, 5 figures. Revised version with minor corrections

The Efimov effect is the only experimentally realized universal phenomenon that exhibits the renormalization-group limit cycle with the three-body parameter parametrizing a family of universality classes. Recent experiments in ultracold atoms have unexpectedly revealed that the three-body parameter itself is universal when measured in units of an effective range. By performing an exact functional renormalization-group analysis with various finite-range interaction potentials, we demonstrate that the onset of the renormalization-group flow into the limit cycle is universal, regardless of short-range details, which connects the missing link between the two universalities of the Efimov physics. A close connection between the topological property of the limit cycle and few-body physics is also delineated., 5 pages, 4 figures

We analyse the low-energy physics of nearly ferromagnetic metals in two spatial dimensions using the functional renormalization group technique. We find a new low-energy fixed point, at which the fermionic (electron-like) excitations are non-Fermi-liquid ($z_f = 13/10$) and the magnetic fluctuations exhibit an anomalous Landau damping whose rate vanishes as $\Gamma_{\bf q} \sim \vert {\bf q} \vert^{3/5}$ in the low-$\vert {\bf q} \vert$ limit. We discuss this renormalization of the Landau-damping exponent, which is the major novel prediction of our work, and highlight the possible link between that renormalization and neutron-scattering data on UGe$_2$ and related compounds. Implications of our analysis for YFe$_2$Al$_{10}$ are also discussed., Comment: 5 pages, 3 figures; action modified to include spin of fermions, resulting in quantitative changes to exponents but same essential physics

We develop a perturbative renormalization-group method in real time to describe nonequilibrium properties of discrete quantum systems coupled linearly to an environment. We include energy broadening and dissipation and develop a cutoff-independent formalism. We present quantitatively reliable results for the nonlinear conductance in the mixed-valence and empty-orbital regime of the nonequilibrium Anderson impurity model with finite on-site Coulomb repulsion., Comment: 4 pages, 4 figures

We demonstrate how to extract all the one-loop renormalization group equations for arbitrary quantum field theories from knowledge of an appropriate Seeley--DeWitt coefficient. By formally solving the renormalization group equations to one loop, we renormalization group improve the classical action, and use this to derive the leading-logarithms in the one-loop effective action for arbitrary quantum field theories., Comment: 4 pages, ReV-TeX 3.1

Following the lead of earlier researchers, we construct a real space renormalization group map for a class of self-organized critical models. We then test a series of quantitative predictions implied by this map against direct simulations of various models. The theory passes four tests, but apparently fails a fifth. We also find that the map has an interesting nongeneric property, suggesting a deeper structure to the theory than previously appreciated. [S0031-9007(98)06840-9]

Starting from a consistency requirement between T-duality symmetry and renormalization group flows, the two-loop metric beta function is found for a d=2 bosonic sigma model on a generic, torsionless background. The result is obtained without Feynman diagram calculations, and represents further evidence that duality symmetry severely constrains renormalization flows., 4 pp., REVTeX. Added discussion on scheme (in)dependence; final version to appear in Phys. Rev. Lett

We study the spin-gap phase in the one-dimensional $t$- $J$ model, assuming that it is caused by the backward scattering process. Based on the renormalization group analysis and symmetry, we can determine the transition point between the Tomonaga-Luttinger liquid and the spin-gap phases, by the level crossing of the singlet and the triplet excitations. In contrast to the previous works, the obtained spin-gap region is unexpectedly large. We also determine that the universality class of the transition belongs to the $k\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ SU(2) Wess-Zumino-Witten model.

We present a novel scheme for an unbiased and non-perturbative treatment of strongly correlated fermions. The proposed approach combines two of the most successful many-body methods, i.e., the dynamical mean field theory (DMFT) and the functional renormalization group (fRG). Physically, this allows for a systematic inclusion of non-local correlations via the flow equations of the fRG, after the local correlations are taken into account non-perturbatively by the DMFT. To demonstrate the feasibility of the approach, we present numerical results for the two-dimensional Hubbard model at half-filling., Comment: 5 pages, 4 figures

We explore the nature of the Bose condensation transition in driven open quantum systems, such as exciton-polariton condensates. Using a functional renormalization group approach formulated in the Keldysh framework, we characterize the dynamical critical behavior that governs decoherence and an effective thermalization of the low frequency dynamics. We identify a critical exponent special to the driven system, showing that it defines a new dynamical universality class. Hence critical points in driven systems lie beyond the standard classification of equilibrium dynamical phase transitions. We show how the new critical exponent can be probed in experiments with driven cold atomic systems and exciton-polariton condensates., 4.5 pages, 1 figure plus 4 pages supplementary material

We investigate the competing Fermi surface instabilities in the Kagome tight-binding model. Specifically, we consider onsite and short-range Hubbard interactions in the vicinity of van Hove filling of the dispersive Kagome bands where the Fermiology promotes the joint effect of enlarged density of states and nesting. The sublattice interference mechanism [Kiesel and Thomale, Phys. Rev. B Rapid Comm., in press.] allows us to explain the intricate interplay between ferromagnetic fluctuations and other ordering tendencies. On the basis of functional renormalization group used to obtain an adequate low-energy theory description, we discover finite angular momentum spin and charge density wave order, a two-fold degenerate d-wave Pomeranchuk instability, and f-wave superconductivity away from van Hove filling. Together, this makes the Kagome Hubbard model the prototypical scenario for several unconventional Fermi surface instabilities., Comment: 4+e pages, 5 figures

The contractor renormalization group (CORE) method, a new approach to solving Hamiltonian lattice systems, is introduced. The method combines contraction and variational techniques with the real-space renormalization group approach. It applies to lattice systems of infinite extent and is ideal for studying phase structure and critical phenomena. The CORE approximation is systematically improvable and can treat systems with dynamical fermions. The method is tested using the (1+1)-dimensional Ising model.

A solution to a given equation is structurally stable if it suffers only an infinitesimal change when the equation (not the solution) is perturbed infinitesimally. We have found that structural stability can be used as a velocity selection principle for propagating fronts. We give examples, using numerical and renormalization group methods., 14 pages, uiucmac.tex, no figures

We investigate the superconducting phase in the K(x)Ba(1-x)Fe2As2 122 compounds from moderate to strong hole-doping regimes. Using the functional renormalization group, we show that, while the system develops a nodeless anisotropic s(±) order parameter in the moderately doped regime, gapping out the electron pockets at strong hole doping drives the system into a nodal (cos k(x) + cos k(y))(cos k(x) - cos k(y)) d-wave superconducting state. This is in accordance with recent experimental evidence from measurements on KFe2As2 which observe a nodal order parameter in the extreme doping regime. The magnetic instability is strongly suppressed.

A linearized tensor renormalization group algorithm is developed to calculate the thermodynamic properties of low-dimensional quantum lattice models. This new approach employs the infinite time-evolving block decimation technique, and allows for treating directly the transfer-matrix tensor network that makes it more scalable. To illustrate the performance, the thermodynamic quantities of the quantum $XY$ spin chain as well as the Heisenberg antiferromagnet on a honeycomb lattice are calculated by the linearized tensor renormalization group method, showing the pronounced precision and high efficiency.

The gravitational asymptotic safety program strives for a consistent and predictive quantum theory of gravity based on a non-trivial ultraviolet fixed point of the renormalization group (RG) flow. We investigate this scenario by employing a novel functional renormalization group equation which takes the causal structure of space-time into account and connects the RG flows for Euclidean and Lorentzian signature by a Wick-rotation. Within the Einstein-Hilbert approximation, the $\beta$-functions of both signatures exhibit ultraviolet fixed points in agreement with asymptotic safety. Surprisingly, the two fixed points have strikingly similar characteristics, suggesting that Euclidean and Lorentzian quantum gravity belong to the same universality class at high energies., Comment: 4 pages, 2 figures

The numerical renormalization group (NRG) is rephrased as a variational method with the cost function given by the sum of all the energies of the effective low-energy Hamiltonian. This allows to systematically improve the spectrum obtained by NRG through sweeping. The ensuing algorithm has a lot of similarities to the density matrix renormalization group (DMRG) when targeting many states, and this synergy of NRG and DMRG combines the best of both worlds and extends their applicability. We illustrate this approach with simulations of a quantum spin chain and a single impurity Anderson model (SIAM) where the accuracy of the effective eigenstates is greatly enhanced as compared to the NRG, especially in the transition to the continuum limit., Comment: As accepted to PRL. Main text: 4 pages, 4 (PDF) figures; Supplementary material: 4 pages, 6 PDF figures; revtex4-1

Real-space renormalization approaches for quantum lattice systems generate certain hierarchical classes of states that are subsumed by the multi-scale entanglement renormalization ansatz (MERA). It is shown that, with the exception of one spatial dimension, MERA states are actually finitely correlated states, i.e., projected entangled pair states (PEPS) with a bond dimension independent of the system size. Hence, real-space renormalization generates states which can be encoded with local effective degrees of freedom, and MERA states form an efficiently contractible class of PEPS that obey the area law for the entanglement entropy. It is shown further that there exist other efficiently contractible schemes violating the area law., Comment: 7 pages, 6 figures; final version, featuring an addendum to the published article

We put forward a scenario that explains the difference between the order-parameter character in arsenide (As) and phosphorous (P) iron-based superconductors. Using functional renormalization group to analyze it in detail, we find that nodal superconductivity on the electron pockets (hole pocket gaps are always nodeless) can naturally appear when the hole pocket at $(\ensuremath{\pi},\ensuremath{\pi})$ in the unfolded Brillouin zone is absent, as is the case in LaOFeP. There, electron-electron interactions render the gap on the electron pockets softly nodal (of ${s}^{\ifmmode\pm\else\textpm\fi{}}$ form). When the pocket of ${d}_{xy}$ orbital character is present, intraorbital interactions with the ${d}_{xy}$ part of the electron Fermi surface drives the superconductivity nodeless.

We introduce a class of states, called minimally entangled typical thermal states (METTS), designed to resemble a typical state of a quantum system at finite temperature with a bias towards classical (minimally entangled) properties. These states reveal in an intuitive way properties such as short-range order which may be hidden in correlation functions. An algorithm is presented which, when used with the density matrix renormalization group (DMRG), is faster by a factor of $10^3 - 10^{10}$ than previous heat-bath approaches for thermally averaged quantities., Comment: 4 pages, 3 figures. v2 has some additional references

We present a simple approximation of the non-perturbative renormalization group designed for the Kardar-Parisi-Zhang equation and show that it yields the correct phase diagram, including the strong-coupling phase with reasonable scaling exponent values in physical dimensions. We find indications of a possible qualitative change of behavior around $d=4$. We discuss how our approach can be systematically improved., Comment: 4 pages, 1 figure, references added, minor changes

In some cases the state of a quantum system with a large number of subsystems can be approximated efficiently by the density matrix renormalization group, which makes use of redundancies in the description of the state. Here we show that the achievable efficiency can be much better when performing density matrix renormalization group calculations in the Heisenberg picture, as only the observable of interest but not the entire state is considered. In some non-trivial cases, this approach can even be exact for finite bond dimensions., version to appear in PRL, acronyms in title and abstract expanded, new improved numerical examples

We apply the fermion functional renormalization group method to determine the pairing symmetry and pairing mechanism of the FeAs-Based materials. Within a five band model with pure repulsive interactions, we find an electronic-driven superconducting pairing instability. For the doping and interaction parameters we have examined, extended s-wave, whose order parameter takes on opposite sign on the electron and hole pockets, is always the most favorable pairing symmetry. The pairing mechanism is the inter Fermi surface Josephson scattering generated by the antiferromagnetic correlation., 4 pages, 4 figures, published version

The multi-scale entanglement renormalisation ansatz (MERA) is argued to provide a natural description for topological states of matter. The case of Kitaev's toric code is analyzed in detail and shown to possess a remarkably simple MERA description leading to distillation of the topological degrees of freedom at the top of the tensor network. Kitaev states on an infinite lattice are also shown to be a fixed point of the RG flow associated with entanglement renormalization. All these results generalize to arbitrary quantum double models., Comment: 6 pages, 17 eps files. v2: References updated, typos corrected. Includes appendix not in published version

In this Letter we show that an arbitrarily good approximation to the propagator ${e}^{itH}$ for a 1D lattice of $n$ quantum spins with Hamiltonian $H$ may be obtained with polynomial computational resources in $n$ and the error $ϵ$ and exponential resources in $|t|$. Our proof makes use of the finitely correlated state or matrix product state formalism exploited by numerical renormalization group algorithms like the density matrix renormalization group. There are two immediate consequences of this result. The first is that Vidal's time-dependent density matrix renormalization group will require only polynomial resources to simulate 1D quantum spin systems for logarithmic $|t|$. The second consequence is that continuous-time 1D quantum circuits with logarithmic $|t|$ can be simulated efficiently on a classical computer, despite the fact that, after discretization, such circuits are of polynomial depth.

Using a functional renormalization group approach we study the zero temperature phase diagram of two-dimensional Bose-Fermi mixtures of ultracold atoms in optical lattices, in the limit when the velocity of bosonic condensate fluctuations is much larger than the Fermi velocity. For spin-1/2 fermions we obtain a phase diagram, which shows a competition of pairing phases of various orbital symmetry (s, p, and d) and antiferromagnetic order. We determine the value of the gaps of various phases close to half filling, and identify subdominant orders as well as short-range fluctuations from the renormalization group flow. For spinless fermions we find that p-wave pairing dominates the phase diagram.

We examine whether cubic non-linearities, allowed by symmetry in the elastic energy of a contact line, may result in a different universality class at depinning. Standard linear elasticity predicts a roughness exponent zeta=1/3 (one loop), zeta=0.39 (numerics) while experiments give zeta of about 0.5. Within functional RG we find that a non-local KPZ-type term is generated at depinning and grows under coarse graining. A fixed point with zeta=0.45 (one loop) is identified, showing that large enough cubic terms increase the roughness. This fixed point is unstable, revealing a rough strong-coupling phase. Experimental study of contact angles theta near pi/2, where cubic terms vanish in the energy, is suggested., 4 pages

Using numerical self-consistent solutions of a sequence of finite replica symmetry breakings (RSB) and Wilson's renormalization group but with the number of RSB steps playing a role of decimation scales, we report evidence for a nontrivial T-->0 limit of the Parisi order function q(x) for the Sherrington-Kirkpatrick spin glass. Supported by scaling in RSB space, the fixed point order function is conjectured to be q*(a)=sqrt[pi]/2 a/xi erf(xi/a) on 0 a at T =0 and xi approximately 1.13+/-0.01. Xi plays the role of a correlation length in a-space. q*(a) may be viewed as the solution of an effective 1D field theory.

The functional renormalization group for the random-field and random-anisotropy O(N) sigma models is studied to 2 loop. The ferromagnetic-disordered (F-D) transition fixed point is found to next order in d = 4 + epsilon for N > N(c) (N(c) = 2.834 740 8 for random field, N(c) = 9.441 21 for random anisotropy). For N < N(c) the lower critical dimension d = d(lc) plunges below d(lc) = 4: we find two fixed points, one describing the quasiordered phase, the other is novel and describes the F-D transition. d(lc) can be obtained in an (N(c)-N) expansion. The theory is also analyzed at large N and a glassy regime is found.

We introduce a picture to analyze the density matrix renormalization group (DMRG) numerical method from a quantum information perspective. This leads to a variational formulation of DMRG which allows for dramatic improvements in the case of problems with periodic boundary conditions. The picture also explains some features of the method in terms of entanglement and teleportation.

We study the antiferromagnetic spin-1/2 Heisenberg model on a two-dimensional bipartite quasiperiodic structure, the octagonal tiling -- the aperiodic equivalent of the square lattice for periodic systems. An approximate block spin renormalization scheme is described for this problem. The ground state energy and local staggered magnetizations for this system are calculated, and compared with the results of a recent Quantum Monte Carlo calculation for the tiling. It is conjectured that the ground state energy is exactly equal to that of the quantum antiferromagnet on the square lattice., Comment: To appear in Physical Review Letters

We consider the properties of vibrational dynamics on random networks, with random masses and spring constants. The localization properties of the eigenstates contrast greatly with the Laplacian case on these networks. We introduce several real-space renormalization techniques which can be used to describe this dynamics on general networks, drawing on strong disorder techniques developed for regular lattices. The renormalization group is capable of elucidating the localization properties, and provides, even for specific network instances, a fast approximation technique for determining the spectra which compares well with exact results., 4 pages, 3 figures

We introduce a method, based on an exact calculation of the effective action at large N, to bridge the gap between mean-field theory and renormalization in complex systems. We apply it to a d-dimensional manifold in a random potential for large embedding space dimension N. This yields a functional renormalization group equation valid for any d, which contains both the O(epsilon=4-d) results of Balents-Fisher and some of the nontrivial results of the Mezard-Parisi solution, thus shedding light on both. Corrections are computed at order O(1/N). Applications to the Kardar-Parisi-Zhang growth model, random field, and mode coupling in glasses are mentioned.

We introduce a computationally stable inverse Monte Carlo renormalization group transformation method that provides a number of advantages for the calculation of critical properties. We are able to simulate the fixed point of a renormalization group for arbitrarily large lattices without critical slowing down. The log-log scaling plots obtained with this method show remarkable linearity, leading to accurate estimates for critical exponents. We illustrate this method with calculations in two- and three-dimensional Ising models for a variety of renormalization group transformations.

We introduce a natural and simple to implement renormalization scheme of the Hartree-Fock-Bogoliubov (HFB) equations for the case of zero range pairing interaction. This renormalization scheme proves to be equivalent to a simple energy cut-off with a position dependent running coupling constant., Comment: 4 pages, 1 figure. The text has changed somewhat, replaced the figure with a different one, however initial assumptions and conclusions remained unchanged

The density-matrix renormalization-group algorithm is extended to treat time-dependent problems. The method provides a systematic and robust tool to explore out-of-equilibrium phenomena in quantum many-body systems. We illustrate the method by showing that attractive interactions enhance the tunneling current between two Luttinger liquids, whereas repulsive interactions suppress it, in qualitative agreement with analytical predictions. Enhancement of the transport current through a quantum dot in the Kondo regime is also exhibited.

A formulation of the Ginzburg-Landau-Wilson version of the partition function of a system with a continuously varying order parameter as a transfer matrix calculation allows for the application of methods based on the Density Matrix Renormalization Group (DMRG) to the calculation of the free energy of the O(1) model. The essence of both the mapping and the DMRG calculation is laid out, along with results that validate this strategy. This method forms the basis of a unified approach to the crossover from three to two dimensions in an O(1) system with a slab-like geometry., ReVTeX, 7 pages, 4 figures in eps format

Made available in DSpace on 2022-04-28T19:56:40Z (GMT). No. of bitstreams: 0 Previous issue date: 1995-01-01 Renormalization group equations for the physical t matrix are written for quantum scattering with some potentials singular at the origin in two and three dimensions. The momentum-space perturbative treatment of these scattering problems exhibits ultraviolet divergences and permits renormalization leading to a scale. These equations yield the correct asymptotic behavior and some low-energy properties of the t matrix. Illustrations are made for the Dirac delta potential in two and three dimensions. © 1995 The American Physical Society. Instituto de Física Teórica, Universidade Estadual Paulista, 01405-900 Sao Paulo Departamento de Física, Instituto Tecnológico de Aeronautica, Centro Técnico Aeroespacial, Sao Paulo Instituto de Física Teórica, Universidade Estadual Paulista, 01405-900 Sao Paulo

We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena are RG equations. The renormalized perturbation approach may be simpler to use than other approaches, because it does not require the use of asymptotic matching, and yields practically superior approximations., Comment: 13 pages, plain tex + uiucmac.tex (available from babbage.sissa.it), one PostScript figure appended at end. Or (easier) get compressed postscript file by anon ftp from gijoe.mrl.uiuc.edu (128.174.119.153), file /pub/rg_sing_prl.ps.Z