arXiv subjects

Jakub Zakrzewski

Publications and source records attributed to Jakub Zakrzewski.

At least 127 records · Page 7Linked to original sources

arXiv2017

Toolbox for Abelian lattice gauge theories with synthetic matter

Fundamental forces of Nature are described by field theories, also known as gauge theories, based on a local gauge invariance. The simplest of them is quantum electrodynamics (QED), which is an example of an Abelian gauge theory. Such theories describe the dynamics of massless photons and their coupling to matter. However, in two spatial dimension (2D) they are known to exhibit gapped phases at low temperature. In the realm of quantum spin systems, it remains a subject of considerable debate if their low energy physics can be described by emergent gauge degrees of freedom. Here we present a class of simple two-dimensional models that admit a low energy description in terms of an Abelian gauge theory. We find rich phase diagrams for these models comprising exotic deconfined phases and gapless phases - a rare example for 2D Abelian gauge theories. The counter-intuitive presence of gapless phases in 2D results from the emergence of additional symmetry in the models. Moreover, we propose schemes to realize our model with current experiments using ultracold bosonic atoms in optical lattices.

cond-mat.quant-gas↗

arXiv2017

Many-body localization due to random interactions

The possibility of observing many body localization of ultracold atoms in a one dimensional optical lattice is discussed for random interactions. In the non-interacting limit, such a system reduces to single-particle physics in the absence of disorder, i.e. to extended states. In effect the observed localization is inherently due to interactions and is thus a genuine many-body effect. In the system studied, many-body localization manifests itself in a lack of thermalization visible in temporal propagation of a specially prepared initial state, in transport properties, in the logarithmic growth of entanglement entropy as well as in statistical properties of energy levels.

cond-mat.quant-gas↗

arXiv2016

Fibonacci anyon excitations of one-dimensional dipolar lattice bosons

We study a system of dipolar bosons in a one-dimensional optical lattice using exact diagonalization and density matrix renormalization group methods. In particular, we analyze low energy properties of the system at an average filling of 3/2 atoms per lattice site. We identify the region of the parameter space where the system has non-Abelian Fibonacci anyon excitations that correspond to fractional domain walls between different charge-density-waves. When such one-dimensional systems are combined into a two-dimensional network, braiding of Fibonacci anyon excitations has potential application for fault tolerant, universal, topological quantum computation. Contrary to previous calculations, our results also demonstrate that super-solid phases are not present in the phase diagram for the discussed 3/2 average filling. Instead, decreasing the value of the nearest-neighbor tunneling strength leads to a direct, Berezinskii-Kosterlitz-Thouless, super-fluid to charge-density-wave quantum phase transition.

cond-mat.str-el↗

arXiv2016

Locating the quantum critical point of the Bose-Hubbard model through singularities of simple observables

We show that the critical point of the two-dimensional Bose-Hubbard model can be easily found through studies of either on-site atom number fluctuations or the nearest-neighbor two-point correlation function (the expectation value of the tunnelling operator). Our strategy to locate the critical point is based on the observation that the derivatives of these observables with respect to the parameter that drives the superfluid-Mott insulator transition are singular at the critical point in the thermodynamic limit. Performing the quantum Monte Carlo simulations of the two-dimensional Bose-Hubbard model, we show that this technique leads to the accurate determination of the position of its critical point. Our results can be easily extended to the three-dimensional Bose-Hubbard model and different Hubbard-like models. They provide a simple experimentally-relevant way of locating critical points in various cold atomic lattice systems.

cond-mat.quant-gas↗

arXiv2016

Different lattice geometries with synthetic dimension

The possibility of creating different geometries with the help of an extra synthetic dimension in optical lattices is studied. Additional linear potential and Raman assisted tunnelings are used to engineer well controlled tunnelings between available states. The great flexibility of the system allows us to obtain different geometries of synthetic lattices with possibility of adding synthetic gauge fields.

cond-mat.quant-gas↗

arXiv2016

Topological Rice-Mele model in an emergent lattice: Exact diagonalization approach

Using exact diagonalization methods we study possible phases in a one dimensional model of two differently populated fermionic species in a periodically driven optical lattice. The shaking amplitude and frequency are chosen to resonantly drive $s-p$ transition while minimizing the standard intraband tunnelings. We numerically verify that in the vicinity of vanishing intraband tunnelings the system, for an appropriate filling, shows an emergent density wave configuration of composites. The majority fermions moving in such a lattice mimic the celebrated Rice-Mele model. Far away from that region structure changes to clustered phase, with intermediate phase abundantly populated by defects of the density wave. These defects lead to loclaized modes carrying fractional particle charge. The results obtained are compared with earlier mean field approximation predictions.

cond-mat.quant-gas↗

arXiv2015

Properties of the one-dimensional Bose-Hubbard model from a high-order perturbative expansion

We employ a high-order perturbative expansion to characterize the ground state of the Mott phase of the one-dimensional Bose-Hubbard model. We compute for different integer filling factors the energy per lattice site, the two-point and density-density correlations, and expectation values of powers of the on-site number operator determining the local atom number fluctuations (variance, skewness, kurtosis). We compare these expansions to numerical simulations of the infinite-size system to determine their range of applicability. We also discuss a new sum rule for the density-density correlations that can be used in both equilibrium and non-equilibrium systems.

cond-mat.quant-gas↗

arXiv2015

Controlling disorder with periodically modulated interactions

We investigate a celebrated problem of one dimensional tight binding model in the presence of disorder leading to Anderson localization from a novel perspective. A binary disorder is assumed to be created by immobile heavy particles for the motion of the lighter, mobile species in the limit of no interaction between mobile particles. Fast periodic modulations of interspecies interactions allow us to produce an effective model with small diagonal and large off-diagonal disorder unexplored in cold atoms experiments. We present an expression for an approximate Anderson localization length and verify the existence of the well known extended resonant mode and analyze the influence of nonzero next-nearest neighbor hopping terms. We point out that periodic modulation of interaction allow disorder to work as a tunable band-pass filter for momenta.

cond-mat.quant-gas↗

arXiv2015

Role of correlations and off-diagonal terms in binary disordered one dimensional systems

We investigate one dimensional tight binding model in the presence of a correlated binary disorder. The disorder is due to the interaction of particles with heavy immobile other species. Off-diagonal disorder is created by means of a fast periodic modulation of interspecies interaction. The method based on transfer matrix techniques allows us to calculate the energies of extended modes in the correlated binary disorder. We focus on $N$-mer correlations and regain known results for the case of purely diagonal disorder. For off-diagonal disorder we find resonant energies. We discuss ambiguous properties of those states and compare analytical results with numerical calculations. Separately we describe a special case of the dual random dimer model.

cond-mat.dis-nn↗

arXiv2015

Time reversals of irreversible quantum maps

We introduce the notion of time reversal in open quantum systems as represented by linear quantum operations, and a related generalization of classical entropy production in the environment. This functional is the ratio of the probability to observe a transition between two states under the forward and the time reversed dynamics, and leads, as in the classical case, to fluctuation relations as tautological identities. As in classical dynamics in contact with a heat bath, time reversal is not unique, and we discuss several possibilities. For any bistochastic map its dual map preserves the trace and describes a legitimate dynamics reversed in time, in that case the entropy production in the environment vanishes. For a generic stochastic map we construct a simple quantum operation which can be interpreted as a time reversal. For instance, the decaying channel, which sends the excited state into the ground state with a certain probability, can be reversed into the channel transforming the ground state into the excited state with the same probability.

quant-ph↗

arXiv2015

Spontaneous magnetization and anomalous Hall effect in an emergent Dice lattice

Ultracold atoms in optical lattices serve as a tool to model different physical phenomena appearing originally in condensed matter. To study magnetic phenomena one needs to engineer synthetic fields as atoms are neutral. Appropriately shaped optical potentials force atoms to mimic charged particles moving in a given field. We present the realization of artificial gauge fields for the observation of anomalous Hall effect. Two species of attractively interacting ultracold fermions are considered to be trapped in a shaken two dimensional triangular lattice. A combination of interaction induced tunneling and shaking can result in an emergent Dice lattice. In such a lattice the staggered synthetic magnetic flux appears and it can be controlled with external parameters. The obtained synthetic fields are non-Abelian. Depending on the tuning of the staggered flux we can obtain either anomalous Hall effect or its quantized version. Our results are reminiscent of Anomalous Hall conductivity in spin-orbit coupled ferromagnets.

cond-mat.quant-gas↗

arXiv2015

Dynamics of heat and mass transport in a quantum insulator

The real time evolution of two pieces of quantum insulators, initially at different temperatures, is studied when they are glued together. Specifically, each subsystem is taken as a Bose-Hubbard model in a Mott insulator state. The process of temperature equilibration via heat transfer is simulated in real time using the Minimally Entangled Typical Thermal States algorithm. The analytic theory based on quasiparticles transport is also given.

cond-mat.quant-gas↗

arXiv2014

Non-standard Hubbard models in optical lattices: a review

Originally, the Hubbard model has been derived for describing the behaviour of strongly-correlated electrons in solids. However, since over a decade now, variations of it are also routinely being implemented with ultracold atoms in optical lattices. We review some of the rich literature on this subject, with a focus on more recent non-standard forms of the Hubbard model. After an introduction to standard (fermionic and bosonic) Hubbard models, we discuss briefly common models for mixtures, as well as the so called extended Bose-Hubbard models, that include interactions between neighboring sites, next-neighboring sites, and so on. The main part of the review discusses the importance of additional terms appearing when refining the tight-binding approximation on the original physical Hamiltonian. Even when restricting the models to the lowest Bloch band is justified, the standard approach neglects the density-induced tunneling (which has the same origin as the usual on-site interaction). The importance of these contributions is discussed for both contact and dipolar interactions. For sufficiently strong interactions, also the effects related to higher Bloch bands become important even for deep optical lattices. Different approaches that aim at incorporating these effects, mainly via dressing the basis Wannier functions with interactions, leading to effective, density-dependent Hubbard-type models, are reviewed. We discuss also examples of Hubbard-like models that explicitly involve higher $p$-orbitals, as well as models that couple dynamically spin and orbital degrees of freedom. Finally, we review mean-field nonlinear-Schrödinger models of the Salerno type that share with the non-standard Hubbard models the nonlinear coupling between the adjacent sites. In that part, discrete solitons are the main subject of the consideration. We conclude by listing some future open problems.

cond-mat.quant-gas↗

arXiv2014

Rice-Mele model with topological solitons in an optical lattice

Attractive ultra-cold fermions trapped in a one-dimensional periodically shaken opticla lattices are considered. For an appropriate resonant shaking the system realizes paradigmatic dimes physics described by Rice-Mele model. The important feature of our system is the possible presence of controlled defects. They result in the creation of topologically protected loclaized modes carrying fractional particle number. Their possible experimental signatures are discussed.

cond-mat.quant-gas↗

arXiv2014

Bose-Hubbard model with random impurities: Multiband and nonlinear hopping effects

We investigate the phase diagrams of theoretical models describing bosonic atoms in a lattice in the presence of randomly localized impurities. By including multiband and nonlinear hopping effects we enrich the standard model containing only the chemical-potential disorder with the site-dependent hopping term. We compare the extension of the MI and the BG phase in both models using a combination of the local mean-field method and a Hartree-Fock-like procedure, as well as, the Gutzwiller-ansatz approach. We show analytical argument for the presence of triple points in the phase diagram of the model with chemical-potential disorder. These triple points however, cease to exists after the addition of the hopping disorder.

cond-mat.quant-gas↗

arXiv2014

One-dimensional s-p superlattice

The physics of one dimensional optical superlattices with resonant $s$-$p$ orbitals is reexamined in the language of appropriate Wannier functions. It is shown that details of the tight binding model realized in different optical potentials crucially depend on the proper determination of Wannier functions. We discuss the properties of a superlattice model which quasi resonantly couples $s$ and $p$ orbitals and show its relation with different tight binding models used in other works.

cond-mat.quant-gas↗

arXiv2014

Numerical studies of ground state fidelity of the Bose-Hubbard model

We compute ground state fidelity of the one-dimensional Bose-Hubbard model at unit filling factor. To this aim, we apply the DMRG algorithm to systems with open and periodic boundary conditions. We find that fidelity differs significantly in the two cases and study its scaling properties in the quantum critical regime.

cond-mat.str-el↗

arXiv2013

Variational Bose-Hubbard model revisited

For strongly interacting bosons in optical lattices the standard description using Bose-Hubbard model becomes questionable. The role of excited bands becomes important. In such a situation we compare results of simulations using multiband Bose-Hubbard model with a recent proposition based on a time dependent variational approach. It is shown that the latter, in its original formulation, uses too small variational space leading often to spurious effects. Possible expansion of variational approach is discussed.

quant-ph↗