arXiv subjects

Mario Collura

Publications and source records attributed to Mario Collura.

At least 73 records · Page 4Linked to original sources

arXiv2019

Ballistic transport and boundary resistances in inhomogeneous quantum spin chains

Transport phenomena are central to physics, and transport in the many-body and fully-quantum regime is attracting an increasing amount of attention. It has been recently revealed that some quantum spin chains support ballistic transport of excitations at all energies. However, when joining two semi-infinite ballistic parts, such as the XX and XXZ spin-1/2 models, our understanding suddenly becomes less established. Employing a matrix-product-state ansatz of the wavefunction, we study the relaxation dynamics in this latter case. Here we show that it takes place inside a light cone, within which two qualitatively different regions coexist: an inner one with a strong tendency towards thermalization, and an outer one supporting ballistic transport. We comment on the possibility that even at infinite time the system supports stationary currents and displays a non-zero Kapitza boundary resistance. Our study paves the way to the analysis of the interplay between transport, integrability, and local defects.

cond-mat.stat-mech↗

arXiv2019

Relaxation of the order-parameter statistics in the Ising quantum chain

We study the out-of-equilibrium probability distribution function of the local order parameter in the transverse field Ising quantum chain. Starting from a fully polarised state, the relaxation of the ferromagnetic order is analysed: we obtain a full analytical description of the late-time stationary distribution by means of a remarkable relation to the partition function of a 3-states classical model. Accordingly, depending on the phase whereto the post-quench Hamiltonian belongs, the probability distribution may locally retain memories of the initial long-range order. When quenching deep in the broken-symmetry phase, we show that the stationary order-parameter statistics is indeed related to that of the ground state. We highlight this connection by inspecting the ground-state equilibrium properties, where we propose an effective description based on the block-diagonal approximation of the $n$-point spin correlation functions.

cond-mat.stat-mech↗

arXiv2019

Suppression of transport in non-disordered quantum spin chains due to confined excitations

The laws of thermodynamics require any initial macroscopic inhomogeneity in extended many-body systems to be smoothed out by the time evolution through the activation of transport processes. In generic, non-integrable quantum systems, transport is expected to be governed by a diffusion law, whereas a sufficiently strong quenched disorder can suppress it completely due to many-body localization of quantum excitations. Here we show that the confinement of quasi-particles can also lead to transport suppression even if the dynamics are generated by homogeneous Hamiltonians. We demonstrate this in the quantum Ising chain with transverse and longitudinal magnetic fields in the paradigmatic case of the evolution of domain-wall states. We perform extensive numerical simulations of the dynamics which turn out to be in excellent agreement with an effective analytical description valid within both weak and strong confinement regimes. Our results show that the energy flow from "hot" to "cold" regions of the chain is suppressed for all accessible times. We argue that this phenomenon is connected with the presence of atypical states in the many-body energy spectrum which violate the eigenstate thermalization hypothesis, as recently reported in the literature.

cond-mat.stat-mech↗

arXiv2019

Hamiltonian truncation approach to quenches in the Ising field theory

In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1+1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations not only for small, but even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while in the paramagnetic phase the single magnon excitation governs the dynamics, allowing us to capture the time evolution of the magnetisation using a combination of known results from perturbation theory and form factor based methods. We point out that the dominance of low lying excitations allows for the numerical or experimental determination of the mass spectra through the study of the quench dynamics.

cond-mat.stat-mech↗

arXiv2019

How order melts after quantum quenches

Injecting a sufficiently large energy density into an isolated many-particle system prepared in a state with long-range order will lead to the melting of the order over time. Detailed information about this process can be derived from the quantum mechanical probability distribution of the order parameter. We study this process for the paradigmatic case of the spin-1/2 Heisenberg XXZ chain. We determine the full quantum mechanical distribution function of the staggered subsystem magnetization as a function of time after a quantum quench from the classical Néel state. This provides a detailed picture of how the Néel order melts and reveals the existence of an interesting regime at intermediate times that is characterized by a very broad probability distribution.

cond-mat.stat-mech↗

arXiv2018

Quantum Quench in a Harmonically Trapped One-Dimensional Bose Gas

We study the non-equilibrium dynamics of a one-dimensional Bose gas trapped by a harmonic potential for a quench from zero to infinite interaction. The different thermodynamic limits required for the equilibrium pre- and post-quench Hamiltonians are the origin of a few unexpected phenomena that have no counterparts in the translational invariant setting. We find that the dynamics is perfectly periodic with breathing time related to the strength of the trapping potential. For very short times, we observe a sudden expansion leading to an extreme dilution of the gas and to the emergence of slowly decaying tails in the density profile. The haste of the expansion induces a undertow effect with a pronounced local minimum of the density at the center of the trap. At half period there is a refocusing phenomenon characterized by a sharp central peak of the density, juxtaposed to algebraically decaying tails. We finally show that the time-averaged density is correctly captured by a generalized Gibbs ensemble built with the conserved mode occupations.

cond-mat.quant-gas↗

arXiv2017

Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions

We consider the nonequilibrium protocol where two semi-infinite gapped XXZ chains, initially prepared in different equilibrium states, are suddenly joint together. At large times, a generalized hydrodynamic description applies, according to which the system can locally be represented by space- and time- dependent stationary states. The magnetization displays an unusual behavior: depending on the initial state, its profile may exhibit abrupt jumps that can not be predicted directly from the standard hydrodynamic equations and which signal non-ballistic spin transport. We ascribe this phenomenon to the structure of the local conservation laws and make a prediction for the exact location of the jumps. We find that the jumps propagate at the velocities of the heaviest quasiparticles. By means of tDMRG simulations we show that our theory yields a complete description of the long-time steady profiles of conserved charges, currents, and local correlations.

cond-mat.stat-mech↗

arXiv2017

Non-equilibrium spin transport in integrable spin chains: persistent currents and emergence of magnetic domains

We construct exact steady states of unitary non-equilibrium time evolution in the gapless XXZ spin-1/2 chain where integrability preserves ballistic spin transport at long-times. We characterize the quasi-local conserved quantities responsible for this feature and introduce a computationally effective way to evaluate their expectation values on generic matrix product initial states. We employ this approach to reproduce the long-time limit of local observables in all quantum quenches which explicitly break particle-hole or time-reversal symmetry. We focus on a class of initial states supporting persistent spin currents and our predictions remarkably agree with numerical simulations at long times. Furthermore, we propose a protocol for this model where interactions, even when antiferromagnetic, are responsible for the unbounded growth of a macroscopic magnetic domain.

cond-mat.str-el↗

arXiv2017

Analytic solution of the Domain Wall non-equilibrium stationary state

We consider the out-of-equilibrium dynamics generated by joining two domains with arbitrary opposite magnetisations. We study the stationary state which emerges by the unitary evolution via the spin $1/2$ XXZ Hamiltonian, in the gapless regime, where the system develops a stationary spin current. Using the generalized hydrodynamic approach, we present a simple formula for the space-time profile of the spin current and the magnetisation exact in the limit of large times. As a remarkable effect, we show that the stationary state has a strongly discontinuous dependence on the strength of interaction. This feature allows us to give a qualitative estimation for the transient behavior of the current which is compared with numerical simulations. Moreover, we analyse the behavior around the edge of the magnetisation profile and we argue that, unlike the XX free-fermionic point, interactions always prevent the emergence of a Tracy-Widom scaling.

cond-mat.stat-mech↗

arXiv2017

Full counting statistics in the spin-1/2 Heisenberg XXZ chain

The spin-1/2 Heisenberg chain exhibits a quantum critical regime characterized by quasi long-range magnetic order at zero temperature. We quantify the strength of quantum fluctuations in the ground state by determining the probability distributions of the components of the (staggered) subsystem magnetization. Some of these exhibit scaling and the corresponding universal scaling functions can be determined by free fermion methods and by exploiting a relation with the boundary sine-Gordon model.

cond-mat.stat-mech↗

arXiv2017

Quenches from gaussian bosons to Tonks-Girardeau gas: stationary states and effects of a confining potential

We consider the general problem of quenching an interacting Bose gas from the noninteracting regime to the strong repulsive case described by the Tonks-Girardeau limit, with the initial state being a gaussian ensemble for the bosons. A generic multi-point correlation function in the steady state can be fully described in terms of a Fredholm-like determinant suitable both for a numerical study and for an analytical study in certain limiting cases. Finally, we extend the study to the presence of a smooth confining potential showing that, in the thermodynamic limit, the time evolution of the two-point function can be mapped to a classical problem in a properly defined phase-space.

cond-mat.stat-mech↗

arXiv2016

Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents

We consider the non-equilibrium time evolution of piecewise homogeneous states in the XXZ spin-1/2 chain, a paradigmatic example of an interacting integrable model. The initial state can be thought as the result of joining chains with different global properties. Through dephasing, at late times the state becomes locally equivalent to a stationary state which explicitly depends on position and time. We propose a kinetic theory of elementary excitations and derive a continuity equation which fully characterizes the thermodynamics of the model. We restrict ourselves to the gapless phase and consider cases where the chains are prepared: 1) at different temperatures; 2) in the ground state of two different models; 3) in the "domain wall" state. We find excellent agreement (any discrepancy is within the numerical error) between theoretical predictions and numerical simulations of time evolution based on TEBD algorithms. As a corollary, we unveil an exact expression for the expectation values of the charge currents in a generic stationary state.

cond-mat.stat-mech↗

arXiv2015

Universal prethermalization dynamics of entanglement entropies after a global quench

We consider the quantum XY model and study the effects of interacting perturbations on the time evolution of the von Neumann and Rényi entropies of spin blocks after global quenches. We show that the entropies are sensitive to perturbations that break hidden symmetries behind the integrability of the model. At times much larger than the characteristic time of the well-known linear increase of the entropies, we identify a time window characterized by a novel linear growth followed by saturation. The typical time of the phenomenon is inversely proportional to the perturbation strength and the behavior is trigger off by the extinction of an infinite number of local conservation laws following a non-abelian algebra. The universality of the crossover is revealed by a semi-classical picture that captures the leading behavior of the entropies. We check our theoretical predictions against iTEBD simulations. The good agreement between theory and numerics substantiates the method developed in [Bertini and Fagotti, J. Stat. Mech. (2015) P07012] for investigating a pre-relaxation limit in weakly interacting models.

cond-mat.stat-mech↗

arXiv2015

Quantum quench within the gapless phase of the spin-1/2 Heisenberg XXZ spin-chain

We consider an interaction quench in the critical spin-1/2 Heisenberg XXZ chain. We numerically compute the time evolution of the two-point correlation functions of spin operators in the thermodynamic limit and compare the results to predictions obtained in the framework of the Luttinger liquid approximation. We find that the transverse correlation function $\langle S^x_jS^x_{j+\ell}\rangle$ agrees with the Luttinger model prediction to a surprising level of accuracy. The agreement for the longitudinal two-point function $\langle S^z_jS^z_{j+\ell}\rangle$ is found to be much poorer. We speculate that this difference between transverse and longitudinal correlations has its origin in the locality properties of the respective spin operator with respect to the underlying fermionic modes.

cond-mat.stat-mech↗

arXiv2014

Interaction quench in a trapped one-dimensional Bose gas

We study the non-equilibrium quench dynamics from free to hard-core one-dimensional bosons in the presence of a hard-wall confining potential. We characterise the density profile and the two-point fermionic correlation function in the stationary state as well as their full time evolution. We find that for long times the system relaxes to a uniform density profile, but the correlation function keeps memory of the initial state with a stationary algebraic long-distance decay as opposite to the exponential behaviour found for the same quench in the periodic setup. We also compute the stationary bosonic two-point correlator which turns out to decay exponentially for large distances. We show that a two-step mechanism governs the time evolution: a quick approach to an almost stationary value is followed by a slow algebraic relaxation to the true stationary state.

cond-mat.quant-gas↗

arXiv2014

Quantum quench from a thermal tensor state: boundary effects and generalized Gibbs ensemble

We consider a quantum quench in a non-interacting fermionic one-dimensional field-theory. The system of size $L$ is initially prepared into two halves $\mathcal{L}$ ($[-L/2,0]$) and $\mathcal{R}$ ($[0,L/2]$), each of them thermalized at two different temperatures, ${T_{L}}$ and ${T_{R}}$ respectively. At a given time the two halves are joined together by a local coupling and the whole system is left to evolve unitarily. For an infinitely extended system ($L\rightarrow \infty$), we show that the time evolution of the particle and energy densities is well described via a hydrodynamic approach which allows us to evaluate the correspondent stationary currents. We show, in such a case, that the two-point correlation functions are deduced, at large times, from a simple non-equilibrium steady state. Otherwise, whenever the boundary conditions are retained (in a properly defined thermodynamic limit), any current is suppressed at large times, and the stationary state is described by a generalized Gibbs ensemble, which is diagonal and depends only on the post-quench mode occupation.

cond-mat.stat-mech↗

arXiv2014

Non-equilibrium transport in $d$-dimensional non-interacting Fermi gases

We consider a non-interacting Fermi gas in $d$ dimensions, both in the non-relativistic and relativistic case. The system of size $L^{d}$ is initially prepared into two halves $\mathcal{L}$ and $\mathcal{R}$, each of them thermalized at two different temperatures, $T_{\mathcal{L}}$ and $T_{\mathcal{R}}$ respectively. At time $t=0$ the two halves are put in contact and the entire system is left to evolve unitarily. We show that, in the thermodynamic limit, the time evolution of the particle and energy densities is perfectly described by a semiclassical approach which permits to analytically evaluate the correspondent stationary currents. In particular, in the case of non-relativistic fermions, we find a low-temperature behavior for the particle and energy currents which is independent from the dimensionality $d$ of the system, being proportional to the difference $T_{\mathcal{L}}^{2}-T_{\mathcal{R}}^{2}$. Only in one spatial dimension ($d=1$), the results for the non-relativistic case agree with the massless relativistic ones.

cond-mat.quant-gas↗

arXiv2014

Relaxation after quantum quenches in the spin-1/2 Heisenberg XXZ chain

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 Néel 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.

cond-mat.stat-mech↗