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We revisit early suggestions to observe spin-charge separation (SCS) in cold-atom settings {in the time domain} by studying one-dimensional repulsive Fermi gases in a harmonic potential, where pulse perturbations are initially created at the center of the trap. We analyze the subsequent evolution using generalized hydrodynamics (GHD), which provides an exact description, at large space-time scales, for arbitrary temperature $T$, particle density, and interactions. At $T=0$ and vanishing magnetic field, we find that, after a nontrivial transient regime, spin and charge dynamically decouple up to perturbatively small corrections which we quantify. In this limit, our results can be understood based on a simple phase-space hydrodynamic picture. At finite temperature, we solve numerically the GHD equations, showing that for low $T>0$ effects of SCS survive and {characterize} explicitly the value of $T$ for which the two distinguishable excitations melt., 12 pages, 7 figures; v2: modified layout; corrected some typos

Entanglement features of the ground state of disordered quantum matter are often captured by an infinite randomness fixed point that, for a variety of models, is the random singlet phase. Although a copious number of studies covers bipartite entanglement in pure states, at present, less is known for mixed states and tripartite settings. Our goal is to gain insights in this direction by studying the negativity spectrum in the random singlet phase. Through the strong disorder renormalization group technique, we derive analytic formulas for the universal scaling of the disorder averaged moments of the partially transposed reduced density matrix. Our analytic predictions are checked against a numerical implementation of the strong disorder renormalization group and against exact computations for the XX spin chain (a model in which free fermion techniques apply). Importantly, our results show that the negativity and logarithmic negativity are not trivially related after the average over the disorder., 15 pages, 3 figures

We study the transport properties of a one-dimensional spinful Fermi gas, after a junction of two semi-infinite subsystems held at different temperatures. The ensuing dynamics is studied by analyzing the space-time profiles of local observables emerging at large distances x and times t, as a function of ζ = x/t. At equilibrium, the system displays two distinct species of quasiparticles, naturally associated with different physical degrees of freedom. By employing the generalized hydrodynamic approach, we show that when the temperatures are finite no notion of separation can be attributed to the quasiparticles. In this case, the profiles can not be qualitatively distinguished by those associated to quasiparticles of a single species that can form bound states. On the contrary, signatures of separation emerge in the low-temperature regime, where two distinct characteristic velocities appear. In this regime, we analytically show that the profiles display a piecewise constant form and can be understood in terms of two decoupled Luttinger liquids.

We consider the time evolution after quantum quenches in the spin-1/2 Heisenberg XXZ quantum spin chain with Ising-like anisotropy. The time evolution of short-distance spin-spin correlation functions is studied by numerical tensor network techniques for a variety of initial states, including N\'eel and Majumdar-Ghosh states and the ground state of the XXZ chain at large values of the anisotropy. The various correlators appear to approach stationary values, which are found to be in good agreement with the results of exact calculations of stationary expectation values in appropriate generalized Gibbs ensembles. In particular, our analysis shows how symmetries of the post-quench Hamiltonian that are broken by particular initial states are restored at late times., Comment: 31 pages, 23 figures

We study the scaling of the Renyi and entanglement entropy of two disjoint blocks of critical Ising models, as function of their sizes and separations. We present analytic results based on conformal field theory that are quantitatively checked in numerical simulations of both the quantum spin chain and the classical two dimensional Ising model. Theoretical results match the ones obtained from numerical simulations only after taking properly into account the corrections induced by the finite length of the blocks to their leading scaling behavior., 4 pages, 5 figures. Revised version accepted for publication in PRB

We determine the crossover exponents associated with the traceless tensorial quadratic field and the third- and fourth-harmonic operators for $O(n)$ vector models by reanalyzing the existing six-loop fixed-dimension series with the pseudo-$ϵ$ expansion. With this approach we obtain accurate theoretical estimates that are in optimum agreement with other theoretical and experimental results.

We investigate the controversial issue of the existence of universality classes describing critical phenomena in three-dimensional statistical systems characterized by a matrix order parameter with symmetry O(2)xO(N) and symmetry-breaking pattern O(2)xO(N) -> O(2)xO(N-2). Physical realizations of these systems are, for example, frustrated spin models with noncollinear order. Starting from the field-theoretical Landau-Ginzburg-Wilson Hamiltonian, we consider the massless critical theory and the minimal-subtraction scheme without epsilon expansion. The three-dimensional analysis of the corresponding five-loop expansions shows the existence of a stable fixed point for N=2 and N=3, confirming recent field-theoretical results based on a six-loop expansion in the alternative zero-momentum renormalization scheme defined in the massive disordered phase. In addition, we report numerical Monte Carlo simulations of a class of three-dimensional O(2)xO(2)-symmetric lattice models. The results provide further support to the existence of the O(2)xO(2) universality class predicted by the field-theoretical analyses.

The critical thermodynamics of the two-dimensional N-vector cubic and MN models is studied within the field-theoretical renormalization-group (RG) approach. The beta functions and critical exponents are calculated in the five-loop approximation and the RG series obtained are resummed using the Borel-Leroy transformation combined with the generalized Pad�� approximant and conformal mapping techniques. For the cubic model, the RG flows for various N are investigated. For N=2 it is found that the continuous line of fixed points running from the XY fixed point to the Ising one is well reproduced by the resummed RG series and an account for the five-loop terms makes the lines of zeros of both beta functions closer to each another. For the cubic model with N\geq 3, the five-loop contributions are shown to shift the cubic fixed point, given by the four-loop approximation, towards the Ising fixed point. This confirms the idea that the existence of the cubic fixed point in two dimensions under N>2 is an artifact of the perturbative analysis. For the quenched dilute O(M) models ($MN$ models with N=0) the results are compatible with a stable pure fixed point for M\geq1. For the MN model with M,N\geq2 all the non-perturbative results are reproduced. In addition a new stable fixed point is found for moderate values of M and N., 26 pages, 3 figures

We compute the crossover exponent $\phi$ describing the crossover from the random-exchange to the random-field critical behavior in Ising systems. For this purpose, we consider the field-theoretical approach based on the replica method, and perform a six-loop calculation in the framework of a fixed-dimension expansion. The crossover from random-exchange to random-field critical behavior has been observed in dilute anisotropic antiferromagnets, such as Fe$_x$Zn$_{1-x}$F$_2$ and Mn$_x$Zn$_{1-x}$F$_2$, when applying an external magnetic field. Our result $\phi=1.42(2)$ for the crossover exponent is in good agreement with the available experimental estimates., Comment: 5 pages

We study the multicritical behavior arising from the competition of two distinct types of ordering characterized by $\mathrm{O}(n)$ symmetries. For this purpose, we consider the renormalization-group flow for the most general $\mathrm{O}{(n}_{1})\ensuremath{\bigoplus}\mathrm{O}{(n}_{2})$-symmetric Landau-Ginzburg-Wilson Hamiltonian involving two fields ${\ensuremath{\varphi}}_{1}$ and ${\ensuremath{\varphi}}_{2}$ with ${n}_{1}$ and ${n}_{2}$ components, respectively. In particular, we determine in which cases, approaching the multicritical point, one may observe the asymptotic enlargement of the symmetry to $\mathrm{O}(N)$ with ${N=n}_{1}{+n}_{2}.$ By performing a five-loop $\ensuremath{\epsilon}$-expansion computation we determine the fixed points and their stability. It turns out that for ${N=n}_{1}{+n}_{2}g~3$ the $\mathrm{O}(N)$-symmetric fixed point is unstable. For $N=3,$ the multicritical behavior is described by the biconal fixed point with critical exponents that are very close to the Heisenberg ones. For $Ng~4$ and any ${n}_{1}{,n}_{2}$ the critical behavior is controlled by the tetracritical decoupled fixed point. We discuss the relevance of these results for some physically interesting systems, in particular for anisotropic antiferromagnets in the presence of a magnetic field and for high-${T}_{c}$ superconductors. Concerning the SO(5) theory of superconductivity, we show that the bicritical O(5) fixed point is unstable with a significant crossover exponent ${\ensuremath{\varphi}}_{4,4}\ensuremath{\approx}0.15;$ this implies that the O(5) symmetry is not effectively realized at the point where the antiferromagnetic and superconducting transition lines meet. The multicritical behavior is either governed by the tetracritical decoupled fixed point or is of first-order type if the system is outside its attraction domain.

We study the combined effect of cubic anisotropy and quenched uncorrelated impurities on multicomponent spin models. For this purpose, we consider the field-theoretical approach based on the Ginzburg-Landau-Wilson $\phi^4$ Hamiltonian with cubic-symmetric quartic interactions and quenched randomness coupled to the local energy density. We compute the renormalization-group functions to six loops in the fixed-dimension (d=3) perturbative scheme. The analysis of such high-order series provides an accurate description of the renormalization-group flow. The results are also used to determine the critical behavior of three-dimensional antiferromagnetic three- and four-state Potts models in the presence of quenched impurities., Comment: 23 pages, 1 figures

We analyze the critical behavior of two-dimensional N-vector spin systems with noncollinear order within the five-loop renormalization-group (RG) approximation. The structure of the RG flow is studied for different N leading to the conclusion that the chiral fixed point governing the critical behavior of physical systems with $N=2$ and $N=3$ does not coincide with that given by the $1/N$ expansion. We show that the stable chiral fixed point for $Nl~{N}^{*},$ including $N=2$ and $N=3,$ turns out to be a focus. We give a complete characterization of the critical behavior controlled by this fixed point, also evaluating the subleading crossover exponents. The spiral-like approach of the chiral fixed point is argued to give rise to unusual crossover and near-critical regimes that may imitate varying critical exponents seen in numerous physical and computer experiments.

We study the critical behavior of frustrated spin models with noncollinear order in two dimensions, including antiferromagnets on a triangular lattice and fully frustrated antiferromagnets. For this purpose we consider the corresponding $O(N)\ifmmode\times\else\texttimes\fi{}O(2)$ Landau-Ginzburg-Wilson (LGW) Hamiltonian and compute the field-theoretic expansion to four loops and determine its large-order behavior. We show the existence of a stable fixed point for the physically relevant cases of two- and three-component spin models. We also give a prediction for the critical exponent $\ensuremath{\eta}$ which is $\ensuremath{\eta}=0.24(6)$ and $\ensuremath{\eta}=0.29(5)$ for $N=3$ and 2, respectively.

How quantum information is scrambled in the global degrees of freedom of non-equilibrium many-body systems is a key question to understand local thermalization. Here we propose that the scaling of the mutual information between two intervals of fixed length as a function of their distance is a diagnostic tool for scrambling after a quantum quench. We consider both integrable and non-integrable one dimensional systems. In integrable systems, the mutual information exhibits an algebraic decay with the distance between the intervals, signalling weak scrambling. This behavior may be qualitatively understood within the quasiparticle picture for the entanglement spreading, predicting, in the scaling limit of large intervals and times, a decay exponent equal to $1/2$. Away from the scaling limit, the power-law behavior persists, but with a larger (and model-dependent) exponent. For non-integrable models, a much faster decay is observed, which can be attributed to the finite life time of the quasiparticles: unsurprisingly, non-integrable models are better scramblers., Comment: 8 pages, 3 figures. Published version

The time evolution of the entanglement entropy is a key concept to understand the structure of a non-equilibrium quantum state. In a large class of models, such evolution can be understood in terms of a semiclassical picture of moving quasiparticles spreading the entanglement throughout the system. However, it is not yet known how the entanglement splits between the sectors of an internal local symmetry of a quantum many-body system. Here, guided by the examples of conformal field theories and free-fermion chains, we show that the quasiparticle picture can be adapted to this goal, leading to a general conjecture for the charged entropies whose Fourier transform gives the desired symmetry resolved entanglement $S_n(q)$. We point out two physically relevant effects that should be easily observed in atomic experiments: a delay time for the onset of $S_n(q)$ which grows linearly with $|\Delta q|$ (the difference from the charge $q$ and its mean value), and an effective equipartition when $|\Delta q|$ is much smaller than the subsystem size., Comment: 7 pages, 2 figures