arXiv subjects

Marcin Mierzejewski

Publications and source records attributed to Marcin Mierzejewski.

At least 37 records · Page 2Linked to original sources

arXiv2018

Reduced-basis approach to many-body localization

Within the standard model of many-body localization, i.e., the disordered chain of spinless fermions, we investigate how the interaction affects the many-body states in the basis of noninteracting localized Anderson states. From this starting point we follow the approach that uses a reduced basis of many-body states. Together with an extrapolation to the full basis, it proves to be efficient for the evaluation of the stiffnesses of local observables, which remain finite within the non-ergodic regime and represent the hallmark of the many-body localization (MBL). The method enables a larger span of system sizes and, within the MBL regime, allows for a more careful analysis of the size scaling of calculated quantities. On the other hand, the survival stiffness as the representative of non--local quantities, reveals limitations of the reduced-basis approach.

cond-mat.str-el↗

arXiv2018

Identification of Majorana Modes in Interacting Systems by Local Integrals of Motion

Recently, there has been substantial progress in methods of identifying local integrals of motion in interacting integrable models or in systems with many-body localization. We show that one of these approaches can be utilized for constructing local, conserved, Majorana fermions in systems with an arbitrary many-body interaction. As a test case, we first investigate a non-interacting Kitaev model and demonstrate that this approach perfectly reproduces the standard results. Then, we discuss how the many-body interactions influence the spatial structure and the lifetime of the Majorana modes. Finally, we determine the regime for which the information stored in the Majorana correlators is also retained for arbitrarily long times at high temperatures. We show that it is included in the regime with topologically protected soft Majorana modes, but in some cases is significantly smaller.

cond-mat.str-el↗

arXiv2017

Complete many-body localization in the t-J model caused by random magnetic field

The many body localization (MBL) of spin-1/2 fermions poses a challenging problem. It is known that the disorder in the charge sector may be insufficient to cause full MBL. Here, we study dynamics of a single hole in one dimensional t-J model subject to a random magnetic field. We show that strong disorder that couples only to the spin sector localizes both spin and charge degrees of freedom. Charge localization is confirmed also for a finite concentration of holes. While we cannot precisely pinpoint the threshold disorder, we conjecture that there are two distinct transitions. Weaker disorder first causes localization in the spin sector. Carriers become localized for somewhat stronger disorder, when the spin localization length is of the order of a single lattice spacing.

cond-mat.str-el↗

arXiv2017

Many-body localization caused by temporal disorder

The many-body localization (MBL) is commonly related to a strong spatial disorder. We show that MBL may alternatively be generated by adding a temporal disorder to periodically driven many-body systems. We reach this conclusion by mapping the evolution of such systems on the dynamics of the time-independent, disordered, Hubbard-like models. Our result opens the way to experimental studies of MBL in systems that reveal crystalline structures in the time domain. In particular, we discuss two relevant setups which can be implemented in experiments on ultra-cold atomic gases.

cond-mat.dis-nn↗

arXiv2017

Counting local integrals of motion in disordered spinless-fermion and Hubbard chains

We develop a procedure which systematically generates all conserved operators in the disordered models of interacting fermions. Among these operators, we identify and count the independent and local integrals of motion (LIOM) which represent the hallmark of the many-body localization (MBL). The method is tested first on the prototype disordered chain of interacting spinless fermions. As expected for full MBL, we find for large enough disorder $N_M=2^M-1$ independent and quasi-local LIOM with support on $M$ consecutive sites. On the other hand, the study of the disordered Hubbard chain reveals that $3^M-1< N_M < 4^M/2$ which is less than required for full MBL but much more than in the case of spinless fermions.

cond-mat.str-el↗

arXiv2017

Delocalized charge carriers in strongly disordered t-J model

We study the influence of the electron-magnon interaction on the particle transport in strongly disordered systems. The analysis is based on results obtained for a single hole in the one-dimensional t-J model. Unless there exists a mechanism that localizes spin excitations, the charge carrier remains delocalized even for a very strong disorder and shows subdiffusive motion up to the longest accessible times. However, upon inspection of the propagation times between neighboring sites as well as a careful finite-size scaling we conjecture that the anomalous subdiffusive transport may be transient and should eventually evolve into a normal diffusive motion.

cond-mat.str-el↗

arXiv2016

Nature of Bosonic Excitations revealed by high-energy charge carriers

We address a long standing problem concerning the origin of bosonic excitations that strongly interact with charge carriers. We show that the time-resolved pump-probe experiments are capable to distinguish between regular bosonic degrees of freedom, e.g. phonons, and the hard-core bosons, e.g., magnons. The ability of phonon degrees of freedom to absorb essentially unlimited amount of energy renders relaxation dynamics nearly independent on the absorbed energy or the fluence. In contrast, the hard core effects pose limits on the density of energy stored in the bosonic subsystems resulting in a substantial dependence of the relaxation time on the fluence and/or excitation energy. Very similar effects can be observed also in a different setup when the system is driven by multiple pulses of equal energy.

cond-mat.str-el↗

arXiv2016

Distinctive response of many-body localized systems to strong electric field

We study systems which are close to or within the many-body localized (MBL) regime and are driven by strong electric field. In the ergodic regime, the disorder extends applicability of the equilibrium linear--response theory to stronger drivings, whereas the response of the MBL systems is very distinctive, revealing currents with damped oscillations. The oscillation frequency is independent of driving and the damping is not due to heating but rather due to dephasing. The details of damping depend on the system's history reflecting nonergodicity of the MBL phase, while the frequency of the oscillations remains a robust hallmark of localization. We show that the distinctive characteristic of the driven MBL phase is also a logarithmic increase of the energy and the polarization with time.

cond-mat.str-el↗

arXiv2015

Approximate conservation laws in perturbed integrable lattice models

We develop a numerical algorithm for identifying approximately conserved quantities in models perturbed away from integrability. In the long-time regime, these quantities fully determine correlation functions of local observables. Applying the algorithm to the perturbed XXZ model we find that the main effect of perturbation consists in expanding the support of conserved quantities. This expansion follows quadratic dependence on the strength of perturbation. The latter result together with correlation functions of conserved quantities obtained from the memory function analysis confirm feasibility of the perturbation theory.

cond-mat.str-el↗

arXiv2015

The Ising version of the t-J model

The t-J model is analysed in the limit of strong anisotropy, where the transverse components of electron spin are neglected. We propose a slave-particle-type approach that is valid, in contradiction to many of the standard approaches, in the low-doping regime and becomes exact for a half-filled system. We describe an effective method that allows to numerically study the system with the no-double-occupancy constraint rigorously taken into account at each lattice site. Then, we use this approach to demonstrate the destruction of the antiferromagnetic order by increasing the doping and formation of Nagaoka polarons in the strong interaction regime.

cond-mat.str-el↗

arXiv2015

Local and Quasilocal Conserved Quantities in Integrable Systems

We outline a procedure for counting and identifying a complete set of local and quasilocal conserved operators in integrable lattice systems. The method yields a systematic generation of all independent, conserved quasilocal operators related to time-average of local operators with a support on up to M consecutive sites. As an example we study the anisotropic Heisenberg spin-1/2 chain and show that the number of independent conserved operators grows linearly with M. Besides the known local operators there exist novel quasilocal conserved quantities in all the parity sectors. The existence of quasilocal conserved operators is shown also for the isotropic Heisenberg model. Implications for the anomalous relaxation of quenched systems are discussed as well.

cond-mat.stat-mech↗

arXiv2015

Reversal of relaxation due to dephasing environment

We show that any finite quantum system $S$ can be coupled to a dephasing environment in such a way that the internal mechanism responsible for relaxation of observables acting on $S$ can be effectively canceled. By adjusting this coupling, the difference between the initial and the long--time expectation values of any observable on $S$ can be tuned to arbitrarily small however nonzero value. This statement is exemplified and visualized by numerical studies of relaxation in a generic one-dimensional system of interacting fermions.

cond-mat.stat-mech↗

arXiv2014

Energy and particle currents in a driven integrable system

We study the ratio of the energy and particle currents ($j^E/j^N$) in an integrable one dimensional system of interacting fermions. Both currents are driven by a finite (nonzero) dc electric field. In doped insulators, where the local conserved quantities saturate the so called Mazur bound on the charge stiffness, $j^E/j^N$ agrees with the linear--response theory, even though such agreement may be violated for each current alone. However, in the metallic regime with a non-saturated Mazur bound, the ratio $j^E/j^N$ in a driven system is shown to be much larger than predicted by the linear--response theory.

cond-mat.str-el↗

arXiv2014

Energy current and energy fluctuations in driven quantum wires

We discuss the energy current and the energy fluctuations in an isolated quantum wire driven far from equilibrium. The system consists of interacting spinless fermions and is driven by a time--dependent magnetic flux. The energy current is defined by the continuity equation for the energy density which is derived both for homogeneous as well as for inhomogeneous systems. Since the total energy is not conserved in the driven system, the continuity equation includes the source terms which are shown to represent the Joule heating effects. For short times and weak drivings the energy current agrees with the linear response theory. For stronger fields or longer times of driving the system enters the quasiequilibrium regime when the energy current gradually diminishes due to the heating effects. Finally, for even stronger driving the energy current is shown to undergo a damped Bloch oscillations. The energy spread also increases upon driving. However, the time--dependence of this quantity in the low field regime is quite unexpected since it is determined mostly by the time of driving being quite independent of the instantaneous energy of the system.

cond-mat.mes-hall↗

arXiv2014

Breakdown of the generalized Gibbs ensemble for current-generating quenches

We establish a relation between two hallmarks of integrable systems: the relaxation towards the generalized Gibbs ensemble (GGE) and the dissipationless charge transport. We show that the former one is possible only if the so called Mazur bound on the charge stiffness is saturated by local conserved quantities. As an example we show how a non--GGE steady state with a current can be generated in the one-dimensional model of interacting spinless fermions with a flux quench. Moreover an extended GGE involving the quasi-local conserved quantities can be formulated for this case.

cond-mat.str-el↗

arXiv2014

Unusual Two-stage Dynamics of the Spin-Lattice Polaron Formation

We follow the formation of a spin-lattice polaron after a quantum quench that simulates absorption of the pump{pulse in the time-resolved experiments. We discover a two-stage relaxation where spin and lattice degrees of freedom represent an integral part of the relaxation mechanism. In the first stage the kinetic energy of the spin-lattice polaron relaxes towards its ground state value while relaxation processes via spin and phonon degrees of freedom remain roughly independent. In the second, typically much longer stage, a subsequent energy transfer between lattice and spin degrees of freedom via the charge carrier emerges. The excess local spin energy radiates away via magnon excitations.

cond-mat.str-el↗

arXiv2011

Coexistence of superconductivity and incommensurate magnetic order

The influence of incommensurate spin density waves (SDW) on superconductivity in unconventional superconductors is studied by means of the Bogolubov-de Gennes (BdG) equations. Exploiting translational symmetries of a magnetically ordered two-dimensional system we propose an approach that allows to solve the BdG equations on much larger clusters than it is usually possible for inhomogeneous systems. Applying this approach we demonstrate that the presence of incommensurate spin density waves induces real-space inhomogeneity of the superconducting order parameter even in the absence of external magnetic field. In this case a homogeneous order parameter of the Bardeen-Cooper-Schrieffer-type superconducting state is slightly modulated, or equivalently, a small fraction of the charge carriers form Cooper pairs with non-zero total momentum. However, when a sufficiently strong magnetic field is applied, the homogeneous component of the order parameter is suppressed and the system transits to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, where the order parameter oscillates changing sign. We show that for s-wave pairing the presence of external magnetic field diminishes the destructive influence of the SDW order on superconductivity. A simple explanation of this effect is also proposed.

cond-mat.supr-con↗

arXiv2011

Integrable Mott insulators driven by finite electric field

We develop a method for extracting the steady nonequilibrium current from studies of driven isolated systems, applying it to the model of one-dimensional Mott insulator at high temperatures. While in the nonintegrable model the nonequilibrium conditions can be accounted by internal heating, the integrability leads to a strongly nonlinear dc response with vanishingly small dc conductivity in the linear--response regime. The finding is consistent with equilibrium results for dc limit of the optical conductivity determined in the presence of a weak and decreasing perturbation.

cond-mat.str-el↗