arXiv subjects

Marko Znidaric

Publications and source records attributed to Marko Znidaric.

At least 37 records · Page 2Linked to original sources

arXiv2019

Exact localized and ballistic eigenstates in disordered chaotic spin ladders and the Fermi-Hubbard model

We demonstrate the existence of exact atypical many-body eigenstates in a class of disordered, interacting one-dimensional quantum systems that includes the Fermi-Hubbard model as a special case. These atypical eigenstates, which generically have finite energy density and are exponentially many in number, are populated by noninteracting excitations. They can exhibit Anderson localization with area-law eigenstate entanglement or, surprisingly, ballistic transport at any disorder strength. These properties differ strikingly from those of typical eigenstates nearby in energy, which we show give rise to diffusive transport as expected in a chaotic quantum system. We discuss how to observe these atypical eigenstates in cold-atom experiments realizing the Fermi-Hubbard model, and comment on the robustness of their properties.

cond-mat.str-el↗

arXiv2019

Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet

Equilibrium spatio-temporal correlation functions are central to understanding weak nonequilibrium physics. In certain local one-dimensional classical systems with three conservation laws they show universal features. Namely, fluctuations around ballistically propagating sound modes can be described by the celebrated Kardar-Parisi-Zhang (KPZ) universality class. Can such universality class be found also in quantum systems? By unambiguously demonstrating that the KPZ scaling function describes magnetization dynamics in the SU(2) symmetric Heisenberg spin chain we show, for the first time, that this is so. We achieve that by introducing new theoretical and numerical tools, and make a puzzling observation that the conservation of energy does not seem to matter for the KPZ physics.

cond-mat.stat-mech↗

arXiv2019

Nonequilibrium steady-state Kubo formula: equality of transport coefficients

We address the question of whether transport coefficients obtained from a unitary closed system setting, i.e., the standard equilibrium Green-Kubo formula, are the same as the ones obtained from a weakly driven nonequilibrium steady-state calculation. We first derive a nonequilibrium Kubo-like expression for the steady-state diffusion constant expressed as a time-integral of either a current or a conserved density nonequilibrium correlation function. This expression has certain advantages over the equilibrium Green-Kubo formula, but is not clear if it gives the same value of the diffusion constant. We then rigorously show that, if the unitary dynamics is diffusive the nonequilibrium formula indeed gives exactly the same transport coefficient. The form of finite-size correction is also predicted. Theoretical results are verified by an explicit calculation of the diffusion constant in several interacting many-body models.

cond-mat.stat-mech↗

arXiv2018

Entanglement in a dephasing model and many-body localization

We study entanglement dynamics in a diagonal dephasing model in which the strength of interaction decays exponentially with distance -- the so-called l-bit model of many-body localization. We calculate the exact expression for entanglement growth with time, finding in addition to a logarithmic growth, a sublogarithmic correction. Provided the l-bit picture correctly describes the many-body localized phase this implies that the entanglement in such systems does not grow (just) as a logarithm of time, as believed so far.

cond-mat.dis-nn↗

arXiv2018

Interaction instability of localization in quasiperiodic systems

Integrable models form pillars of theoretical physics because they allow for full analytical understanding. Despite being rare, many realistic systems can be described by models that are close to integrable. Therefore, an important question is how small perturbations influence the behavior of solvable models. This is particularly true for many-body interacting quantum systems where no general theorems about their stability are known. Here, we show that no such theorem can exist by providing an explicit example of a one-dimensional many-body system in a quasiperiodic potential whose transport properties discontinuously change from localization to diffusion upon switching on interaction. This demonstrates an inherent instability of a possible many-body localization in a quasiperiodic potential at small interactions. We also show how the transport properties can be strongly modified by engineering potential at only a few lattice sites.

cond-mat.str-el↗

arXiv2018

Asymmetry in energy versus spin transport in certain interacting, disordered systems

We study energy transport in XXZ spin chains driven to nonequilibrium configurations by thermal reservoirs of different temperatures at the boundaries. We discuss the transition between diffusive and subdiffusive transport regimes in sectors of zero and finite magnetization at high temperature. At large anisotropies we find that diffusive energy transport prevails over a large range of disorder strengths, which is in contrast to spin transport that is subdiffusive in the same regime for weak disorder strengths. However, when finite magnetization is induced, both energy and spin currents decay as a function of system size with the same exponent. Based on this, we conclude that diffusion of energy is much more pervasive than that of magnetization in these disordered spin-1/2 systems, and occurs across a significant range of the interaction-disorder parameter phase-space; we suggest this is due to conservation laws present in the clean XXZ limit.

cond-mat.dis-nn↗

arXiv2017

A class of states supporting diffusive spin dynamics in the isotropic Heisenberg model

The spin transport in isotropic Heisenberg model in the sector with zero magnetization is generically super-diffusive. Despite that, we here demonstrate that for a specific set of domain-wall-like initial product states it can instead be diffusive. We theoretically explain the time evolution of such states by showing that in the limiting regime of weak spatial modulation they are approximately product states for very long times, and demonstrate that even in the case of larger spatial modulation the bipartite entanglement entropy grows only logarithmically in time. In the limiting regime we derive a simple closed equation governing the dynamics, which in the continuum limit and for the initial step magnetization profile results in a solution expressed in terms of Fresnel integrals.

cond-mat.str-el↗

arXiv2017

Fractality in nonequilibrium steady states of quasiperiodic systems

We investigate the nonequilibrium response of quasiperiodic systems to boundary driving. In particular we focus on the Aubry-André-Harper model at its metal-insulator transition and the diagonal Fibonacci model. We find that opening the system at the boundaries provides a transparent and experimentally viable technique to probe its underlying fractality, which is reflected in the fractal spatial dependence of simple observables (such as magnetization) in the nonequilibrium steady state. We also find that the dynamics in the nonequilibrium steady state depends on the length of the chain chosen: generic length chains harbour qualitatively slower transport (different scaling exponent) than Fibonacci length chains, which is in turn slower than in the closed system. We conjecture that such fractal nonequilibrium steady states should arise in generic driven critical systems that have fractal properties.

cond-mat.dis-nn↗

arXiv2017

Spin diffusion from an inhomogeneous quench in an integrable system

Generalised hydrodynamics predicts universal ballistic transport in integrable lattice systems when prepared in generic inhomogeneous initial states. However, the ballistic contribution to transport can vanish in systems with additional discrete symmetries. Here we perform large scale numerical simulations of spin dynamics in the anisotropic Heisenberg $XXZ$ spin $1/2$ chain starting from an inhomogeneous mixed initial state which is symmetric with respect to a combination of spin-reversal and spatial reflection. In the isotropic and easy-axis regimes we find non-ballistic spin transport which we analyse in detail in terms of scaling exponents of the transported magnetisation and scaling profiles of the spin density. While in the easy-axis regime we find accurate evidence of normal diffusion, the spin transport in the isotropic case is clearly super-diffusive, with the scaling exponent very close to $2/3$, but with universal scaling dynamics which obeys the diffusion equation in nonlinearly scaled time.

cond-mat.stat-mech↗

arXiv2016

Diffusive and subdiffusive spin transport in the ergodic phase of a many-body localizable system

We study high temperature spin transport in a disordered Heisenberg chain in the ergodic regime. By employing a density matrix renormalization group technique for the study of the stationary states of the boundary-driven Lindblad equation we are able to study extremely large systems (400 spins). We find both a diffusive and a subdiffusive phase depending on the strength of the disorder and on the anisotropy parameter of the Heisenberg chain. Studying finite-size effects we show numerically and theoretically that a very large crossover length exists that controls the passage of a clean-system dominated dynamics to one observed in the thermodynamic limit. Such a large length scale, being larger than the sizes studied before, explains previous conflicting results. We also predict spatial profiles of magnetization in steady states of generic nondiffusive systems.

cond-mat.dis-nn↗

arXiv2016

Influence of dephasing on many-body localization

We study the effects of dephasing noise on a prototypical many-body localized system -- the XXZ spin 1/2 chain with a disordered magnetic field. At times longer than the inverse dephasing strength the dynamics of the system is described by a probabilistic Markov process on the space of diagonal density matrices, while all off-diagonal elements of the density matrix decay to zero. The generator of the Markovian process is a bond-disordered spin chain. The scaling variable is identified, and independence of relaxation on the interaction strength is demonstrated. We show that purity and von Neumann entropy are extensive, showing no signatures of localization, while the operator space entanglement entropy exhibits a logarithmic growth with time until the final saturation corresponding to localization breakdown, suggesting a many-body localized dynamics of the effective Markov process.

cond-mat.str-el↗

arXiv2016

Dissipative remote-state preparation in an interacting medium

Standard quantum state preparation methods work by preparing a required state locally and then distributing it to a distant location by a free-space propagation. We instead study procedures of preparing a target state at a remote location in the presence of an interacting background medium on which no control is required, manipulating only local dissipation. In mathematical terms, we characterize a set of reduced steady states stabilizable by local dissipation. An explicit local method is proposed by which one can construct a wanted one-site reduced steady state at an arbitrary remote site in a lattice of any size and geometry. In the chain geometry we also prove uniqueness of such a steady state. We demonstrate that the convergence time to fixed precision is smaller than the inverse gap, and we study robustness of the scheme in different medium interactions.

quant-ph↗

arXiv2015

Relaxation times of dissipative many-body quantum systems

We study relaxation times, also called mixing times, of quantum many-body systems described by a Lindblad master equation. We in particular study the scaling of the spectral gap with the system length, the so-called dynamical exponent, identifying a number of transitions in the scaling. For systems with bulk dissipation we generically observe different scaling for small and for strong dissipation strength, with a critical transition strength going to zero in the thermodynamic limit. We also study a related phase transition in the largest decay mode. For systems with only boundary dissipation we show a generic bound that the gap can not be larger than 1/L. In integrable systems with boundary dissipation one typically observes scaling 1/L^3, while in chaotic ones one can have faster relaxation with the gap scaling as 1/L and thus saturating the generic bound. We also observe transition from exponential to algebraic gap in systems with localized modes.

cond-mat.stat-mech↗

arXiv2015

Geometry of local quantum dissipation and fundamental limits to local cooling

We geometrically characterize one-qubit dissipators of a Lindblad type. An efficient parametrization in terms of 6 linear parameters opens the way to various optimizations with local dissipation. As an example, we study maximal steady-state singlet fraction that can be achieved with an arbitrary local dissipation and two qubit Hamiltonian. We show that this singlet fraction has a discontinuity as one moves from unital to non-unital dissipators and demonstrate that the largest possible singlet fraction is approximately 0.654. This means that for systems with a sufficiently entangled ground state there is a fundamental quantum limit to the lowest attainable energy. With local dissipation one is unable to cool the system below some limiting non-zero temperature.

quant-ph↗

arXiv2014

Anomalous nonequilibrium current fluctuations in the Heisenberg model

We study fluctuation properties of a one-dimensional anisotropic Heisenberg model out of equilibrium, focusing in particular on the gapped regime. Within the open-system setting we study large-deviation properties of the spin current. Numerically evaluating the first four current cumulants in a nonequilibrium stationary state at high energies, we find that the first two cumulants scale with the system size in a diffusive way, while the 3rd and the 4th cumulants do not. This means that the model is not an ordinary diffusive spin conductor.

cond-mat.str-el↗

arXiv2014

Large-deviation statistics of a diffusive quantum spin chain and the additivity principle

Using the large-deviation formalism, we study the statistics of current fluctuations in a diffusive nonequilibrium quantum spin chain. The boundary-driven XX chain with dephasing consists of a coherent bulk hopping and a local dissipative dephasing. We analytically calculate the exact expression for the second current moment in a system of any length and then numerically demonstrate that in the thermodynamic limit higher-order cumulants and the large-deviation function can be calculated using the additivity principle or macroscopic hydrodynamic theory. This shows that the additivity principle can also hold in systems that are not purely stochastic, and can in particular be valid in quantum systems. We also show that in large systems the current fluctuations are the same as in the classical symmetric simple exclusion process.

cond-mat.stat-mech↗

arXiv2014

A universal set of qubit quantum channels

We investigate the set of quantum channels acting on a single qubit. We provide an alternative, compact generalization of the Fujiwara-Algoet conditions for complete positivity to non-unital qubit channels, which we then use to characterize the possible geometric forms of the pure output of the channel. We provide universal sets of quantum channels for all unital qubit channels as well as for all extremal (not necessarily unital) qubit channels, in the sense that all qubit channels in these sets can be obtained by concatenation of channels in the corresponding universal set. We also show that our universal sets are essentially minimal.

quant-ph↗

arXiv2014

Translationally invariant conservation laws of local Lindblad equations

We study the conditions under which one can conserve local translationally invariant operators by local translationally invariant Lindblad equations in one-dimensional rings of spin-1/2 particles. We prove that for any 1-local operator (e.g., particle density) there exist Lindblad dissipators that conserve that operator, while on the other hand we prove that among 2-local operators (e.g., energy density) only trivial ones of the Ising type can be conserved, while all the other cannot be conserved, neither locally nor globally, by any 2- or 3-local translationally invariant Lindblad equation. Our statements hold for rings of any finite length larger than some minimal length determined by the locality of Lindblad equation. These results show in particular that conservation of energy density in interacting systems is fundamentally more difficult than conservation of 1-local quantities.

quant-ph↗