arXiv subjects

J. Sirker

Publications and source records attributed to J. Sirker.

At least 37 records · Page 2Linked to original sources

arXiv2018

Does a distinct quasi many-body localized phase exist? A numerical study of a translationally invariant system in the thermodynamic limit

We consider a quench in an infinite spin ladder describing a system with two species of bosons in the limit of strong interactions. If the heavy bosonic species has infinite mass the model becomes a spin chain with quenched binary disorder which shows true Anderson localization (AL) or many-body localization (MBL). For finite hopping amplitude $J'$ of the heavy particles, on the other hand, we find an exponential polarization decay with a relaxation rate which depends monotonically on $J'$. Furthermore, the entanglement entropy changes from a constant (AL) or logarithmic (MBL) scaling in time $t$ for $J'=0$ to a sub-ballistic power-law, $S_{\textrm{ent}}\sim t^α$ with $α< 1$, for finite $J'$. We do not find a distinct regime in time where the dynamics for $J'\neq 0$ shows the characteristics of an MBL phase. Instead, we discover a time regime with distinct dephasing and entanglement times, different both from a localized and a fully ergodic phase.

cond-mat.dis-nn↗

arXiv2018

The spin Drude weight of the XXZ chain and generalized hydrodynamics

Based on a generalized free energy we derive exact thermodynamic Bethe ansatz formulas for the expectation value of the spin current, the spin current-charge, charge-charge correlators, and consequently the Drude weight. These formulas agree with recent conjectures within the generalized hydrodynamics formalism. They follow, however, directly from a proper treatment of the operator expression of the spin current. The result for the Drude weight is identical to the one obtained 20 years ago based on the Kohn formula and TBA. We numerically evaluate the Drude weight for anisotropies $Δ=\cos(γ)$ with $γ= nπ/m$, $n\leq m$ integer and coprime. We prove, furthermore, that the high-temperature asymptotics for general $γ=πn/m$---obtained by analysis of the quantum transfer matrix eigenvalues---agrees with the bound which has been obtained by the construction of quasi-local charges.

cond-mat.stat-mech↗

arXiv2018

The fate of dynamical phase transitions at finite temperatures and in open systems

When a quantum system is quenched from its ground state, the time evolution can lead to non-analytic behavior in the return rate at critical times $t_c$. Such dynamical phase transitions (DPT's) can occur, in particular, for quenches between phases with different topological properties in Gaussian models. In this paper we discuss Loschmidt echos generalized to density matrices and obtain results for quenches in closed Gaussian models at finite temperatures as well as for open system dynamics described by a Lindblad master equation. While cusps in the return rate are always smoothed out by finite temperatures we show that dissipative dynamics can be fine-tuned such that DPT's persist.

cond-mat.stat-mech↗

arXiv2017

A bulk-boundary correspondence for dynamical phase transitions in one-dimensional topological insulators and superconductors

We study the Loschmidt echo for quenches in open one-dimensional lattice models with symmetry protected topological phases. For quenches where dynamical quantum phase transitions do occur we find that cusps in the bulk return rate at critical times tc are associated with sudden changes in the boundary contribution. For our main example, the Su-Schrieffer-Heeger model, we show that these sudden changes are related to the periodical appearance of two eigenvalues close to zero in the dynamical Loschmidt matrix. We demonstrate, furthermore, that the structure of the Loschmidt spectrum is linked to the periodic creation of long-range entanglement between the edges of the system.

cond-mat.stat-mech↗

arXiv2017

Current reversals and metastable states in the infinite Bose-Hubbard chain with local particle loss

We present an algorithm which combines the quantum trajectory approach to open quantum systems with a density-matrix renormalization group scheme for infinite one-dimensional lattice systems. We apply this method to investigate the long-time dynamics in the Bose-Hubbard model with local particle loss starting from a Mott-insulating initial state with one boson per site. While the short-time dynamics can be described even quantitatively by an equation of motion (EOM) approach at the mean-field level, many-body interactions lead to unexpected effects at intermediate and long times: local particle currents far away from the dissipative site start to reverse direction ultimately leading to a metastable state with a total particle current pointing away from the lossy site. An alternative EOM approach based on an effective fermion model shows that the reversal of currents can be understood qualitatively by the creation of holon-doublon pairs at the edge of the region of reduced particle density. The doublons are then able to escape while the holes move towards the dissipative site, a process reminiscent---in a loose sense---of Hawking radiation.

cond-mat.quant-gas↗

arXiv2017

Localization of fermions in coupled chains with identical disorder

We study fermionic ladders with identical disorder along the leg direction. Following recent experiments we focus, in particular, on how an initial occupation imbalance evolves in time. By considering different initial states and different ladder geometries we conclude that in generic cases interchain coupling leads to a destruction of the imbalance over time, both for Anderson and for many-body localized systems.

cond-mat.dis-nn↗

arXiv2017

Many-body localization in infinite chains

We investigate the phase transition between an ergodic and a many-body localized phase in infinite anisotropic spin-$1/2$ Heisenberg chains with binary disorder. Starting from the Néel state, we analyze the decay of antiferromagnetic order $m_s(t)$ and the growth of entanglement entropy $S_{\textrm{ent}}(t)$ during unitary time evolution. Near the phase transition we find that $m_s(t)$ decays exponentially to its asymptotic value $m_s(\infty)\neq 0$ in the localized phase while the data are consistent with a power-law decay at long times in the ergodic phase. In the localized phase, $m_s(\infty)$ shows an exponential sensitivity on disorder with a critical exponent $ν\sim 0.9$. The entanglement entropy in the ergodic phase grows subballistically, $S_{\textrm{ent}}(t)\sim t^α$, $α\leq 1$, with $α$ varying continuously as a function of disorder. Exact diagonalizations for small systems, on the other hand, do not show a clear scaling with system size and attempts to determine the phase boundary from these data seem to overestimate the extent of the ergodic phase.

cond-mat.dis-nn↗

arXiv2016

Entanglement entropy of disordered quantum chains following a global quench

We numerically investigate the growth of the entanglement entropy S_{ent}(t) in time t---after a global quench from a product state---in quantum chains with various kinds of disorder. The main focus is, in particular, on fermionic chains with bond disorder. In the noninteracting case at criticality we numerically test recent predictions by the real space renormalization group for the entanglement growth in time, the maximal entanglement as a function of block size, and the decay of a density wave order parameter. We show that multiprecision calculations are required to reach the scaling regime and perform such calculations for specific cases. For interacting models with binary bond disorder we present data based on infinite size density matrix renormalization group calculations and exact diagonalizations. We obtain first numerical evidence for a many-body localized phase in bond disordered systems where S_{ent}(t)~ln t$ seems to hold. Our results for bond disorder are contrasted with the well studied case of potential disorder.

cond-mat.str-el↗

arXiv2015

Propagation of a single hole defect in the one-dimensional Bose-Hubbard model

We study nonequilibrium dynamics in the one-dimensional Bose-Hubbard model starting from an initial product state with one boson per site and a single hole defect. We find that for parameters close to the quantum critical point, the hole splits into a core showing a very slow diffusive dynamics, and a fast mode which propagates ballistically. Using an effective fermionic model at large Hubbard interactions U, we show that the ballistic mode is a consequence of an interference between slow holon and fast doublon dynamics, which occurs once the hole defect starts propagating into the bosonic background at unit filling. Within this model, the signal velocity of the fast ballistic mode is given by the maximum slope of the dispersion of the doublon quasiparticle in good agreement with the numerical data. Furthermore, we contrast this global quench with the dynamics of a single hole defect in the ground state of the Bose-Hubbard model and show that the dynamics in the latter case is very different even for large values of U. This can also be seen in the entanglement entropy of the time evolved states which grows much more rapidly in time in the global quench case.

cond-mat.str-el↗

arXiv2014

Purification and many-body localization in cold atomic gases

We propose to observe many-body localization in cold atomic gases by realizing a Bose-Hubbard chain with binary disorder and studying its non-equilibrium dynamics. In particular, we show that measuring the difference in occupation between even and odd sites, starting from a prepared density-wave state, provides clear signatures of localization. As hallmarks of the many-body localized phase we confirm, furthermore, a logarithmic increase of the entanglement entropy in time and Poissonian level statistics. Our numerical density-matrix renormalization group calculations for infinite system size are based on a purification approach; this allows us to perform the disorder average exactly, thus producing data without any statistical noise and with maximal simulation times of up to a factor 10 longer than in the clean case.

cond-mat.dis-nn↗

arXiv2014

Low temperature dynamics of nonlinear Luttinger liquids

We generalize nonlinear Luttinger liquid theory to describe the dynamics of one-dimensional quantum critical systems at low temperatures. Analyzing density-matrix renormalization group results for the spin autocorrelation function in the XXZ chain we provide, in particular, direct evidence for spin diffusion in sharp contrast to the exponential decay in time predicted by conventional Luttinger liquid theory. Furthermore, we discuss how the frequencies and exponents of the oscillatory contributions from the band edges are renormalized by irrelevant interactions and obtain excellent agreement between our finite temperature nonlinear Luttinger liquid theory and the numerical data.

cond-mat.str-el↗

arXiv2014

Exactly conserved quasilocal operators for the XXZ spin chain

We extend T. Prosen's construction of quasilocal conserved quantities for the XXZ model [Phys. Rev. Lett. 106, 217206 (2011)] to the case of periodic boundary conditions. These quasilocal operators stem from a two-parameter transfer matrix which employs a highest-weight representation of the quantum group algebra inherent in the Yang-Baxter algebra. In contrast with the open chain, where the conservation law is weakly violated by boundary terms, the quasilocal operators in the periodic chain exactly commute with the Hamiltonian and other local conserved quantities.

cond-mat.stat-mech↗

arXiv2014

Boundary Fidelity and Entanglement in the symmetry protected topological phase of the SSH model

We present a detailed study of the fidelity, the entanglement entropy, and the entanglement spectrum, for a dimerized chain of spinless fermions---a simplified Su-Schrieffer-Heeger (SSH) model---with open boundary conditions which is a well-known example for a model supporting a symmetry protected topological (SPT) phase. In the non-interacting case the Hamiltonian matrix is tridiagonal and the eigenvalues and -vectors can be given explicitly as a function of a single parameter which is known analytically for odd chain lengths and can be determined numerically in the even length case. From a scaling analysis of these data for essentially semi-infinite chains we obtain the fidelity susceptibility and show that it contains a boundary contribution which is different in the topologically ordered than in the topologically trivial phase. For the entanglement spectrum and entropy we confirm predictions from massive field theory for a block in the middle of an infinite chain but also consider blocks containing the edge of the chain. For the latter case we show that in the SPT phase additional entanglement---as compared to the trivial phase---is present which is localized at the boundary. Finally, we extend our study to the dimerized chain with a nearest-neighbour interaction using exact diagonalization, Arnoldi, and density-matrix renormalization group methods and show that a phase transition into a topologically trivial charge-density wave phase occurs.

cond-mat.str-el↗

arXiv2014

Locality and thermalization in closed quantum systems

We derive a necessary and sufficient condition for the thermalization of a local observable in a closed quantum system which offers an alternative explanation, independent of the eigenstate thermalization hypothesis, for the thermalization process. We also show that this approach is useful to investigate thermalization based on a finite-size scaling of numerical data. The condition follows from an exact representation of the observable as a sum of a projection onto the local conserved charges of the system and a projection onto the non-local ones. We show that thermalization requires that the time average of the latter part vanishes in the thermodynamic limit while time and statistical averages for the first part are identical. As an example, we use this thermalization condition to analyze exact diagonalization data for a one-dimensional spin model. We find that local correlators do thermalize in the thermodynamic limit although we find no indications that the eigenstate thermalization hypothesis applies.

cond-mat.stat-mech↗

arXiv2014

Dynamical quantum phase transitions and the Loschmidt echo: A transfer matrix approach

A boundary transfer matrix formulation allows to calculate the Loschmidt echo for one-dimensional quantum systems in the thermodynamic limit. We show that non-analyticities in the Loschmidt echo and zeros for the Loschmidt amplitude in the complex plane (Fisher zeros) are caused by a crossing of eigenvalues in the spectrum of the transfer matrix. Using a density-matrix renormalization group algorithm applied to these transfer matrices we numerically investigate the Loschmidt echo and the Fisher zeros for quantum quenches in the XXZ model with a uniform and a staggered magnetic field. We give examples---both in the integrable and the non-integrable case---where the Loschmidt echo does not show non-analyticities although the quench leads across an equilibrium phase transition, and examples where non-analyticities appear for quenches within the same phase. For a quench to the free fermion point, we analytically show that the Fisher zeros sensitively depend on the initial state and can lie exactly on the real axis already for finite system size. Furthermore, we use bosonization to analyze our numerical results for quenches within the Luttinger liquid phase.

cond-mat.str-el↗

arXiv2014

Conducting fixed points for inhomogeneous quantum wires: a conformally invariant boundary theory

Inhomogeneities and junctions in wires are natural sources of scattering, and hence resistance. A conducting fixed point usually requires an adiabatically smooth system. One notable exception is "healing", which has been predicted in systems with special symmetries, where the system is driven to the homogeneous fixed point. Here we present theoretical results for a different type of conducting fixed point which occurs in inhomogeneous wires with an abrupt jump in hopping and interaction strength. We show that it is always possible to tune the system to an unstable conducting fixed point which does not correspond to translational invariance. We analyze the temperature scaling of correlation functions at and near this fixed point and show that two distinct boundary exponents appear, which correspond to different effective Luttinger liquid parameters. Even though the system consists of two separate interacting parts, the fixed point is described by a single conformally invariant boundary theory. We present details of the general effective bosonic field theory including the mode expansion and the finite size spectrum. The results are confirmed by numerical quantum Monte Carlo simulations on spinless fermions. We predict characteristic experimental signatures of the local density of states near junctions.

cond-mat.str-el↗

arXiv2013

The Two-Band Luttinger Liquid with Spin-Orbit Coupling: Applications to Monatomic Chains on Surfaces

Recently, monatomic chains on surfaces have been synthesized which show evidence of Luttinger liquid physics. The experimental data point to a dispersion along the chain with four Fermi points. Here we investigate a general low-energy effective Hamiltonian for such a two-band model where SU(2) spin symmetry is broken but time reversal symmetry persists, as is expected due to the surface geometry. Spin-orbit coupling gives rise to a new energy scale epsilon_{SO} much smaller than the Fermi energy epsilon_F and to spin non-conserving scattering processes. We derive the generic phase diagram at zero temperature as well as an effective phase diagram at temperatures epsilon_{SO} < T << epsilon_F. For the part of the phase diagram where a Luttinger liquid is found to be stable, the density of states and the spectral function are calculated and discussed in relation to the experimental data.

cond-mat.str-el↗

arXiv2013

Closed and Open System Dynamics in a Fermionic Chain with a Microscopically Specified Bath: Relaxation and Thermalization

We study thermalization in a one-dimensional quantum system consisting of a noninteracting fermionic chain with each site of the chain coupled to an additional bath site. Using a density matrix renormalization group algorithm we investigate the time evolution of observables in the chain after a quantum quench. For low densities we show that the intermediate time dynamics can be quantitatively described by a system of coupled equations of motion. For higher densities our numerical results show a prethermalization for local observables at intermediate times and a full thermalization to the grand canonical ensemble at long times. For the case of a weak bath-chain coupling we find, in particular, a Fermi momentum distribution in the chain in equilibrium in spite of the seemingly oversimplified bath in our model.

cond-mat.stat-mech↗