arXiv subjects

Achilleas Lazarides

Publications and source records attributed to Achilleas Lazarides.

At least 37 records · Page 2Linked to original sources

arXiv2019

On time crystallinity in dissipative Floquet systems

We investigate the conditions under which periodically driven quantum systems subject to dissipation exhibit a stable subharmonic response. Noting that coupling to a bath introduces not only cooling but also noise, we point out that a system subject to the latter for the entire cycle tends to lose coherence of the subharmonic oscillations, and thereby the long-time temporal symmetry breaking. We provide an example of a short-ranged two-dimensional system which does not suffer from this and therefore displays persistent subharmonic oscillations stabilised by the dissipation. We also show that this is fundamentally different from the disordered DTC previously found in closed systems, both conceptually and in its phenomenology. The framework we develop here clarifies how fully connected models constitute a special case where subharmonic oscillations are stable in the thermodynamic limit.

cond-mat.stat-mech↗

arXiv2019

Many-body quantum dynamics of initially trapped systems due to a Stark potential --- thermalization vs. Bloch oscillations

We analyze the dynamics of an initially trapped cloud of interacting quantum particles on a lattice under a linear (Stark) potential. We reveal a dichotomy: initially trapped interacting systems possess features typical of both many-body-localized and self-thermalizing systems. We consider both fermions ($t$-$V$ model) and bosons (Bose-Hubbard model). For the zero and infinite interaction limits, both systems are integrable: we provide analytic solutions in terms of the moments of the initial cloud shape, and clarify how the recurrent dynamics (many-body Bloch oscillations) depends on the initial state. Away from the integrable points, we identify and explain the time scale at which Bloch oscillations decohere.

cond-mat.quant-gas↗

arXiv2018

Nonequilibrium quantum order at infinite temperature: spatiotemporal correlations and their generating functions

Localisation-protected quantum order extends the idea of symmetry breaking and order in ground states to individual eigenstates at arbitrary energy. Examples include many-body localised static and $π$-spin glasses in Floquet systems. Such order is inherently dynamical and difficult to detect as the order parameter typically varies randomly between different eigenstates, requiring specific superpositions of eigenstates to be targeted by the initial state. We show that two-time correlators overcome this, reflecting the presence or absence of eigenstate order even in fully-mixed, $infinite$ $temperature$ states. We show how spatiotemporal correlators are generated by the recently introduced dynamical potentials, demonstrating this explicitly using an Ising and a Floquet $π$-spin glass and focusing on features mirroring those of equilibrium statistical mechanics such as bimodal potentials in the symmetry-broken phase.

cond-mat.dis-nn↗

arXiv2017

(Quasi)Periodic revivals in periodically driven interacting quantum systems

Recently it has been shown that interparticle interactions\emph ongenerically\emph default destroy dynamical localization in periodically driven systems, resulting in diffusive transport and heating. In this work we rigorously construct a family of interacting driven systems which are dynamically localized and effectively decoupled from the external driving potential. We show that these systems exhibit tunable periodic or quasiperiodic revivals of the many-body wavefunction and thus\emph onof all\emph default physical observables. By numerically examining spinless fermions on a one dimensional lattice we show that the analytically obtained revivals of such systems remain stable for finite systems with open boundary conditions while having a finite lifetime in the presence of static spatial disorder. We find this lifetime to be inversely proportional to the disorder strength.

cond-mat.dis-nn↗

arXiv2017

Dynamical potentials for non-equilibrium quantum many-body phases

Out of equilibrium phases of matter exhibiting order in individual eigenstates, such as many-body localised spin glasses and discrete time crystals, can be characterised by inherently dynamical quantities such as spatiotemporal correlation functions. In this work, we introduce dynamical potentials which act as generating functions for such correlations and capture eigenstate phases and order. These potentials show formal similarities to their equilibrium counterparts, namely thermodynamic potentials. We provide three representative examples: a disordered, many-body localised XXZ chain showing many-body localisation, a disordered Ising chain exhibiting spin-glass order and its periodically-driven cousin exhibiting time-crystalline order.

cond-mat.stat-mech↗

arXiv2017

Absence of dynamical localization in interacting driven systems

Using a numerically exact method we study the stability of dynamical localization to the addition of interactions in a periodically driven isolated quantum system which conserves only the total number of particles. We find that while even infinitesimally small interactions destroy dynamical localization, for weak interactions density transport is significantly suppressed and is asymptotically diffusive, with a diffusion coefficient proportional to the interaction strength. For systems tuned away from the dynamical localization point, even slightly, transport is dramatically enhanced and within the largest accessible systems sizes a diffusive regime is only pronounced for sufficiently small detunings.

cond-mat.str-el↗

arXiv2017

The fate of a discrete time crystal in an open system

Following the recent realisation that periodically driven quantum matter can support new types of spatiotemporal order, now known as discrete time crystals (DTCs), we consider the stability of this phenomenon. Motivated by its conceptual importance as well as its experimental relevance we consider the effect of coupling to an external environment. We use this to argue, both analytically and numerically, that the DTC in disordered one-dimensional systems is destroyed at long times by any such natural coupling. This holds true even in the case where the coupling is such that the system is prevented from heating up by an external thermal bath.

cond-mat.stat-mech↗

arXiv2016

On the phase structure of driven quantum systems

Clean and interacting periodically driven quantum systems are believed to exhibit a single, trivial "infinite-temperature" Floquet-ergodic phase. In contrast, here we show that their disordered Floquet many-body localized counterparts can exhibit distinct ordered phases delineated by sharp transitions. Some of these are analogs of equilibrium states with broken symmetries and topological order, while others - genuinely new to the Floquet problem - are characterized by order and non-trivial periodic dynamics. We illustrate these ideas in driven spin chains with Ising symmetry.

cond-mat.dis-nn↗

arXiv2016

How periodic driving heats a disordered quantum spin chain

We study the energy absorption in real time of a disordered quantum spin chain subjected to coherent monochromatic periodic driving. We determine characteristic fingerprints of the well-known ergodic (Floquet-ETH for slow driving/weak disorder) and many-body localized (Floquet-MBL for fast driving/strong disorder) phases. In addition, we identify an intermediate regime, where the energy density of the system -- unlike the entanglement entropy a local and bounded observable -- grows logarithmically slowly over a very large time window.

cond-mat.stat-mech↗

arXiv2016

Parafermion chain with $2π/k$ Floquet edge modes

We study parafermion chains with $\mathbb{Z}_k$ symmetry subject to a periodic binary drive. We focus on the case $k=3$. We find that the chains support different Floquet edge modes at nontrivial quasienergies, distinct from those for the static system. We map out the corresponding phase diagram by a combination of analytics and numerics, and provide the location of $2π/3$ modes in parameter space. We also show that the modes are robust to weak disorder. While the previously studied $\mathbb{Z}_2$-invariant Majorana systems posesses a transparent weakly interacting case where the existence of a $π$-Majorana mode is manifest, our intrinsically strongly interacting generalization demonstrates that the existence of such a limit is not necessary.

cond-mat.stat-mech↗

arXiv2015

Fate of many-body localization under periodic driving

We study many-body localised quantum systems subject to periodic driving. We find that the presence of a mobility edge anywhere in the spectrum is enough to lead to delocalisation for any driving strength and frequency. By contrast, for a fully localised many-body system, a delocalisation transition occurs at a finite driving frequency. We present numerical studies on a system of interacting one-dimensional bosons and the quantum random energy model, as well as simple physical pictures accounting for those results.

cond-mat.stat-mech↗

arXiv2014

Periodic thermodynamics of isolated systems

The nature of the behaviour of an isolated many-body quantum system periodically driven in time has been an open question since the beginning of quantum mechanics. After an initial transient, such a system is known to synchronize with the driving; in contrast to the non-driven case, no fundamental principle has been proposed for constructing the resulting non-equilibrium state. Here, we analytically show that, for a class of integrable systems, the relevant ensemble is constructed by maximizing an appropriately defined entropy subject to constraints, which we explicitly identify. This result constitutes a generalisation of the concepts of equilibrium statistical mechanics to a class of far-from-equilibrium-systems, up to now mainly accessible using ad-hoc methods.

cond-mat.stat-mech↗

arXiv2014

Equilibrium states of generic quantum systems subject to periodic driving

When a closed quantum system is driven periodically with period $T$, it approaches a periodic state synchronized with the drive in which any local observable measured stroboscopically approaches a steady value. For integrable systems, the resulting behaviour is captured by a periodic version of a generalized Gibbs ensemble. By contrast, here we show that for generic non-integrable interacting systems, local observables become independent of the initial state entirely. Essentially, this happens because Floquet eigenstates of the driven system at quasienergy $ω_α$ consist of a mixture of the exponentially many eigenstates of the undriven Hamiltonian which are thus drawn from the entire extensive undriven spectrum. This is a form of equilibration which depends only on the Hilbert space of the undriven system and not on any details of its Hamiltonian.

cond-mat.stat-mech↗

arXiv2012

Sticky Normal-Superconductor Interface

We study the quantum Goos-Hänchen(GH) effect for wave-packet dynamics at a normal/superconductor (NS) interface. We find that the effect is amplified by a factor $(E_F/Δ)$, with $E_F$ the Fermi energy and $Δ$ the gap. Interestingly, the GH effect appears only as a time delay $δt$ without any lateral shift, and the corresponding delay length is about $(E_F/Δ)λ_F$, with $λ_F$ the Fermi wavelength. This makes the NS interface "sticky" when $Δ\ll E_F$, since typically GH effects are of wavelength order. This "sticky" behavior can be further enhanced by a resonance mode in NSNS interface. Finally, for a large $Δ$, the resonance-mode effect makes a transition from Andreev to the specular electron reflection as the width of the sandwiched superconductor is reduced.

cond-mat.supr-con↗

arXiv2012

Strongly interacting bosons in multi-chromatic potentials supporting mobility edges: localization, quasi-condensation and expansion dynamics

We provide an account of the static and dynamic properties of hard-core bosons in a one-dimensional lattice subject to a multi-chromatic quasiperiodic potential for which the single-particle spectrum has mobility edges. We use the mapping from strongly interacting bosons to weakly interacting fermions, and provide exact numerical results for hard-core bosons in and out of equilibrium. In equilibrium, we find that the system behaves like a quasi-condensate (insulator) depending on whether the Fermi surface of the corresponding fermionic system lies in a spectral region where the single-particle states are delocalized (localized). We also study non-equilibrium expansion dynamics of initially trapped bosons, and demonstrate that the extent of partial localization is determined by the single-particle spectrum.

cond-mat.quant-gas↗

arXiv2012

Influence of boundary conditions on quantum escape

It has recently been established that quantum statistics can play a crucial role in quantum escape. Here we demonstrate that boundary conditions can be equally important - moreover, in certain cases, may lead to a complete suppression of the escape. Our results are exact and hold for arbitrarily many particles.

quant-ph↗

arXiv2012

Strongly interacting one-dimensional bosons in arbitrary-strength optical lattices: from Bose-Hubbard to sine-Gordon and beyond

We analyze interacting one-dimensional bosons in the continuum, subject to a periodic sinusoidal potential of arbitrary depth. Variation of the lattice depth tunes the system from the Bose-Hubbard limit for deep lattices, through the sine-Gordon regime of weak lattices, to the complete absence of a lattice. Using the Bose-Fermi mapping between strongly interacting bosons and weakly interacting fermions, we derive the phase diagram in the parameter space of lattice depth and chemical potential. This extends previous knowledge from tight-binding (Bose-Hubbard) studies in a new direction which is important because the lattice depth is a readily adjustable experimental parameter. Several other results (equations of state, energy gaps, profiles in harmonic trap) are presented as corollaries to the physics contained in this phase diagram. Generically, both incompressible (gapped) and compressible phases coexist in a trap; this has implications for experimental measurements.

cond-mat.quant-gas↗

arXiv2011

Trapped Two-Dimensional Fermi Gases with Population Imbalance

We study population imbalanced Fermi mixtures under quasi-two-dimensional confinement at zero temperature. Using mean-field theory and the local-density approximation, we study the ground state configuration throughout the BEC-BCS crossover. We find the trapped system to be either fully normal or to consist of a superfluid core surrounded by a normal shell, which is itself either fully or partially polarized. Upon changing the trap imbalance, the trap configuration may undergo continuous transitions between the different ground states. Finally, we argue that thermal equilibration throughout the trap will be considerably slowed down at low temperatures when a superfluid phase is present.

cond-mat.other↗