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We make a systematic study of symmetry-protected topological gapped phases of quantum spin chains in the presence of the frieze space groups in one dimension using matrix product states. Here, the spatial symmetries of the one-dimensional lattice are considered together with an additional 'vertical reflection', which we take to be an on-site $\mathbb{Z}_2$ symmetry. We identify seventeen distinct non-trivial phases, define canonical forms, and compare the topological indices obtained from the MPS analysis with the group cohomological predictions. We furthermore construct explicit renormalization group fixed-point wave functions for symmetry-protected topological phases with global on-site symmetries, possibly combined with time-reversal and parity symmetry. En route, we demonstrate how group cohomology can be computed using the Smith normal form., 13 + 2 pages, submitted to Physical Review B

We construct a constant depth quantum circuit that maps between Morita equivalent string-net models. Due to its constant depth and unitarity, the circuit cannot alter the topological order, which demonstrates that Morita equivalent string-nets are in the same phase. The circuit is constructed from an invertible bimodule category connecting the two input fusion categories of the relevant string-net models, acting as a generalized Fourier transform for fusion categories. The circuit does not only act on the ground state subspace, but acts unitarily on the full Hilbert space when supplemented with ancillas., Comment: 11+2 pages, v2: updated section III.B

Variational Monte Carlo studies employing projected entangled-pair states (PEPS) have recently shown that they can provide answers on long-standing questions such as the nature of the phases in the two-dimensional $J_1 - J_2$ model. The sampling in these Monte Carlo algorithms is typically performed with Markov Chain Monte Carlo algorithms employing local update rules, which often suffer from long autocorrelation times and interdependent samples. We propose a sampling algorithm that generates independent samples from a PEPS, bypassing all problems related to finite autocorrelation times. This algorithm is a generalization of an existing direct sampling algorithm for unitary tensor networks. We introduce an auxiliary probability distribution from which independent samples can be drawn, and combine it with importance sampling in order to evaluate expectation values accurately. We benchmark our algorithm on the classical Ising model and on variational optimization of two-dimensional quantum spin models.

We carry out density functional theory (DFT) calculations to explore the antiferromagnetic (AFM) spin cycloid in multiferroic ${\mathrm{BiFeO}}_{3}$ of the $R3c$ ground state structure. We calculate the energy dispersion $E(\mathbf{q})$ of cycloidal spin spirals along the high symmetry directions of the pseudo-cubic unit cell and find a flat AFM spin spiral (or cycloid) ground state with a periodicity of $\ensuremath{\sim}80$ nm, which is in good agreement with experiments. To investigate which structural distortion of the $R3c$ phase is the driving mechanism for the stabilization of this cycloid, we further study three artificial phases: cubic, $R\overline{3}c$, and $R3m$. In all cases, we find a large exchange frustration. The comparison between these phases provides detailed insight about how polarization and octahedral antiphase tilting affect the different magnetic interactions and the magnetic ground state in ${\mathrm{BiFeO}}_{3}$. In $R3c\phantom{\rule{4pt}{0ex}}{\mathrm{BiFeO}}_{3}$, the magnetic ground state is driven by a competition between the frustrated exchange stemming from the hybridization between the elements Bi, Fe, O and the Dzyaloshinskii-Moriya (DM) interaction due to the Fe-Bi ferroelectric displacement. The cycloid appears to be stable because the anisotropy energy in $R3c\phantom{\rule{4pt}{0ex}}{\mathrm{BiFeO}}_{3}$ is relatively small to enforce a collinear order.

Based on the matrix product state (MPS) formalism, we introduce an ansatz for capturing excited states in finite systems with open boundary conditions, providing a very efficient method for computing, e.g., the spectral gap of quantum spin chains. This method can be straightforwardly implemented on top of an existing density-matrix renormalization group or MPS ground-state code. Although this approach is built on open-boundary MPSs, we also apply it to systems with periodic boundary conditions. Despite the explicit breaking of translation symmetry by the MPS representation, we show that momentum emerges as a good quantum number and can be exploited for labeling excitations on top of MPS ground states. We apply our method to the critical Ising chain on a ring and the classical Potts model on a cylinder. Finally, we apply the same idea to compute excitation spectra for 2D quantum systems on infinite cylinders. Again, despite the explicit breaking of translation symmetry in the periodic direction, we recover momentum as a good quantum number for labeling excitations. We apply this method to the 2D transverse-field Ising model and the half-filled Hubbard model; for the latter, we obtain accurate results for, e.g., the hole dispersion for cylinder circumferences up to eight sites.

The Seebeck coefficient is one of the key ingredients in thermoelectric properties, and it is often calculated based simply on the electronic band structure, within the frame of Boltzmann's transport theory and the constant relaxation time approximation. Despite the simplicity and popularity of this approximation, its validity is not fully justified even in lightly doped semiconductors, and it breaks down completely in metals. On the other hand, more sophisticated first-principles approaches are available but require the computation of the full electron-phonon coupling. Here, we demonstrate with several simple (alkali and noble) metals viz., Li, Na, K, Cu, Ag, Au, and Pt, that the variational approach based on ab initio couplings can reproduce experimental Seebeck coefficients quantitatively, whereas the constant relaxation time approximation yields significant quantitative discrepancies and often fails to predict the correct sign. Calculations of the electrical resistivity of these metals via the variational approach are also reported.

Physical review / B covering condensed matter and materials physics 102(4), 041101 (2020). doi:10.1103/PhysRevB.102.041101, We report the results of an ultrafast, direct structural measurement of optically pumped phonons in a Cr thin film using ultrashort x-ray pulses from a free-electron laser. In addition to measuring and confirming the known long-wavelength dispersion relation of Cr along a particular acoustic branch, we are able to determine the relative phase of the phonons as they are generated. The Cr sample exhibits two generation mechanisms for the phonons: the releasing of a preexisting charge density wave at higher frequencies, and the creation of an acoustic strain pulse via laser heating that dominates at lower frequencies. For the latter mechanism, we are able to measure the frequency dependence of the time required to generate the phonons. To explain the observed magnitude and slope of the delays, we perform first-principles simulations in the framework of density functional perturbation theory and ab initio molecular dynamics to fit anharmonic phonon models. These results show that the wave-vector dependence of the electron-phonon coupling is the driving mechanism behind the delay times: Phase-space limitation leads to higher times near the zone center. The absolute magnitudes of the delay times measured are found to be much shorter than the equilibrium electron-phonon coupling times we compute, indicating that the coupling strength is greatly enhanced when the electronic system is out of equilibrium with the lattice, as has been seen in bismuth and other systems., Published by Inst., Woodbury, NY

We describe a new approach to compute the electron-phonon self-energy and carrier mobilities in semiconductors. Our implementation does not require a localized basis set to interpolate the electron-phonon matrix elements, with the advantage that computations can be easily automated. Scattering potentials are interpolated on dense q meshes using Fourier transforms and ab initio models to describe the long-range potentials generated by dipoles and quadrupoles. To reduce significantly the computational cost, we take advantage of crystal symmetries and employ the linear tetrahedron method and double-grid integration schemes, in conjunction with filtering techniques in the Brillouin zone. We report results for the electron mobility in Si, GaAs, and GaP obtained with this new methodology., G.B., G.-M.R., and G.H. acknowledge financial support from F.R.S.-FNRS. H.P.C.M. acknowledges financial support from F.R.S.-FNRS through the PDR Grants HTBaSE (T.1071.15). M.G., M.J.V., and X.G. acknowledge financial support from F.R.S.-FNRS through the PDR Grants AIXPHO (T.0238.13) and ALPS (T.0103.19). M.J.V. thanks FNRS and ULiege for a sabbatical grant in ICN2. M.S. and M.R. acknowledge the support of Ministerio de Economia, Industria y Competitividad (MINECO-Spain) through Grants No. MAT2016-77100-C2-2-P and No. SEV-2015-0496; of Generalitat de Catalunya (Grant No. 2017 SGR1506); and of the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 724529).

We develop and benchmark a technique for simulating excitation spectra of generic two-dimensional quantum lattice systems using the framework of projected entangled-pair states (PEPS). The technique relies on a variational ansatz for capturing quasiparticle excitations on top of a PEPS ground state. Our method perfectly captures the quasiparticle dispersion relation of the square-lattice transverse-field Ising model, and reproduces the spin-wave velocity and the spin-wave anomaly in the square-lattice Heisenberg model with high precision.

The interplay of magnons and phonons can induce strong temperature variations in the magnetic exchange interactions, leading to changes in the magnetothermal response. This is a central mechanism in many magnetic phenomena, and in the new field of Spin Caloritronics, which focuses on the combination of heat and spin currents. Boson model systems have previously been developed to describe the magnon phonon coupling, but until recently studies rely on empirical parameters. In this work we propose a first principles approach to describe the dependence of the magnetic exchange integrals on phonon renormalization, leading to changes in the magnon dispersion as a function of temperature. The temperature enters into the spin dynamics (by introducing fluctuations) as well as in the magnetic exchange itself. Depending on the strength of the coupling, these two temperatures may or may not be equilibrated, yielding different regimes. We test our approach in typical and well known ferromagnetic materials: Ni, Fe, and Permalloy. We compare our results to recent experiments on the spin-wave stiffness, and discuss departures from Bloch’s law and parabolic dispersion.

We combine the Density Matrix Renormalization Group (DMRG) with Matrix Product State tangent space concepts to construct a variational algorithm for finding ground states of one dimensional quantum lattices in the thermodynamic limit. A careful comparison of this variational uniform Matrix Product State algorithm (VUMPS) with infinite Density Matrix Renormalization Group (IDMRG) and with infinite Time Evolving Block Decimation (ITEBD) reveals substantial gains in convergence speed and precision. We also demonstrate that VUMPS works very efficiently for Hamiltonians with long range interactions and also for the simulation of two dimensional models on infinite cylinders. The new algorithm can be conveniently implemented as an extension of an already existing DMRG implementation., 20 pages + 12 pages appendix, V. Zauner-Stauber previously also published under the name V. Zauner

We study thermal states of strongly interacting quantum spin chains and prove that those can be represented in terms of convex combinations of matrix product states. Apart from revealing new features of the entanglement structure of Gibbs states our results provide a theoretical justification for the use of White's algorithm of minimally entangled typical thermal states. Furthermore, we shed new light on time dependent matrix product state algorithms which yield hydrodynamical descriptions of the underlying dynamics., Comment: v3: 10 pages, 2 figures, final published version

We develop methods to probe the excitation spectrum of topological phases of matter in two spatial dimensions. Applying these to the Fibonacci string nets perturbed away from exact solvability, we analyze a topological phase transition driven by the condensation of non-Abelian anyons. Our numerical results illustrate how such phase transitions involve the spontaneous breaking of a topological symmetry, generalizing the traditional Landau paradigm. The main technical tool is the characterization of the ground states using tensor networks and the topological properties using matrix-product-operator symmetries. The topological phase transition manifests itself by symmetry breaking in the entanglement degrees of freedom of the quantum transfer matrix.

We investigate the chemical bonding characteristics of the transition metal dichalcogenides based on their static and dynamical atomic charges within Density Functional Theory. The dynamical charges of the trigonal transition metal dichalcogenides are anomalously large, while in their hexagonal counterparts, their sign is even counterintuitive i.e. the transition metal takes the negative charge. This phenomenon cannot be understood simply in terms of a change in the static atomic charge as it results from a local change of polarization. We present our theoretical understanding of these phenomena based on the perturbative response of the system to a static electric field and by investigating the hybridization of the molecular orbitals near the Fermi level. Furthermore, we establish a link between the sign of the Born effective charge and the $\pi$-backbonding in organic chemistry and propose an experimental procedure to verify the calculated sign of the dynamical charge in the transition metal dichalcogenides., Comment: 3 figures, 6 pages

We develop the formalism of fermionic matrix product states (fMPS) and show how irreducible fMPS fall in two different classes, related to the different types of simple ${\mathbb{Z}}_{2}$ graded algebras, which are physically distinguished by the absence or presence of Majorana edge modes. The local structure of fMPS with Majorana edge modes also implies that there is always a twofold degeneracy in the entanglement spectrum. Using the fMPS formalism, we make explicit the correspondence between the ${\mathbb{Z}}_{8}$ classification of time-reversal-invariant spinless superconductors and the modulo 8 periodicity in the representation theory of real Clifford algebras. Studying fMPS with general onsite unitary and antiunitary symmetries allows us to define invariants that label symmetry-protected phases of interacting fermions. The behavior of these invariants under stacking of fMPS is derived, which reveals the group structure of such interacting phases. We also consider spatial symmetries and show how the invariant phase factor in the partition function of reflection-symmetric phases on an unorientable manifold appears in the fMPS framework.