arXiv subjects

Balázs Dóra

Publications and source records attributed to Balázs Dóra.

At least 55 records · Page 3Linked to original sources

arXiv2022

Correlations at PT-symmetric quantum critical point

We consider a PT-symmetric Fermi gas with an exceptional point, representing the critical point between PT-symmetric and symmetry broken phases. The low energy spectrum remains linear in momentum and is identical to that of a hermitian Fermi gas. The fermionic Green's function decays in a power law fashion for large distances, as expected from gapless excitations, albeit the exponent is reduced from $-1$ due to the quantum Zeno effect. In spite of the gapless nature of the excitations, the ground state entanglement entropy saturates to a finite value, independent of the subsystem size due to the non-hermitian correlation length intrinsic to the system. Attractive or repulsive interaction drives the system into the PT-symmetry broken regime or opens up a gap and protects PT-symmetry, respectively. Our results challenge the concept of universality in non-hermitian systems, where quantum criticality can be masked due to non-hermiticity.

cond-mat.str-el↗

arXiv2022

Kubo formula for non-Hermitian systems and tachyon optical conductivity

Linear response theory plays a prominent role in various fields of physics and provides us with extensive information about the thermodynamics and dynamics of quantum and classical systems. Here we develop a general theory for the linear response in non-Hermitian systems with non-unitary dynamics and derive a modified Kubo formula for the generalized susceptibility for arbitrary (Hermitian and non-Hermitian) system and perturbation. As an application, we evaluate the dynamical response of a non-Hermitian, one-dimensional Dirac model with imaginary and real masses, perturbed by a time-dependent electric field. The model has a rich phase diagram, and in particular, features a tachyon phase, where excitations travel faster than an effective speed of light. Surprisingly, we find that the dc conductivity of tachyons is finite, and the optical sum rule is exactly satisfied for all masses. Our results highlight the peculiar properties of the Kubo formula for non-Hermitian systems and are applicable for a large variety of settings.

cond-mat.quant-gas↗

arXiv2021

Time dependent electric transport in nodal-loop semimetals

Close to the Fermi energy, nodal loop semimetals have a torus-shaped, strongly anisotropic Fermi surface which affects their transport properties. Here we investigate the non-equilibrium dynamics of nodal loop semimetals by going beyond linear response and determine the time evolution of the current after switching on a homogeneous electric field. The current grows monotonically with time for electric fields perpendicular to the nodal loop plane however it exhibits non-monotonical behavior for field orientations aligned within the plane. After an initial non-universal growth $\sim Et$, the current first reaches a plateau $\sim E$. Then, for perpendicular directions, it increases while for in-plane directions it decreases with time to another plateau, still $\sim E$. These features arise from interband processes. For long times or strong electric fields, the current grows as $\sim E^{3/2}t$ or $\sim E^3t^2$ for perpendicular or parallel electric fields, respectively. This non-linear response represents an intraband effect where the large number of excited quasiparticles responds to the electric field. Our analytical results are benchmarked by the numerical evaluation of the current from continuum and tight-binding models of nodal loop semimetals.

cond-mat.mes-hall↗

arXiv2021

Defect production due to time-dependent coupling to environment in the Lindblad equation

Recently defect production was investigated during non-unitary dynamics due to non-Hermitian Hamiltonian. By ramping up the non-Hermitian coupling linearly in time through an exceptional point, defects are produced in much the same way as approaching a Hermitian critical point. A generalized Kibble--Zurek scaling accounted for the ensuing scaling of the defect density in terms of the speed of the drive and the corresponding critical exponents. Here we extend this setting by adding the recycling term and considering the full Lindbladian time evolution of the problem with quantum jumps. We find that by linearly ramping up the environmental coupling in time, and going beyond the steady-state solution of the Liouvillian, the defect density scales linearly with the speed of the drive for all cases. This scaling is unaffected by the presence of exceptional points of the Liouvillian, which can show up in the transient states. By using a variant of the adiabatic perturbation theory, the scaling of the defect density is determined exactly from a set of algebraic equations. Our study indicates the distinct sensitivity of the Lindbladian time evolution to exceptional points corresponding to steady states and transient states.

quant-ph↗

arXiv2021

Non-Hermitian Lindhard function and Friedel oscillations

The Lindhard function represents the basic building block of many-body physics and accounts for charge response, plasmons, screening, Friedel oscillation, RKKY interaction etc. Here we study its non-Hermitian version in one dimension, where quantum effects are traditionally enhanced due to spatial confinement, and analyze its behavior in various limits of interest. Most importantly, we find that the static limit of the non-Hermitian Lindhard function has no divergence at twice the Fermi wavenumber and vanishes identically for all other wavenumbers at zero temperature. Consequently, no Friedel oscillations are induced by a non-Hermitian, imaginary impurity to lowest order in the impurity potential at zero temperature. Our findings are corroborated numerically on a tight-binding ring by switching on a weak real or imaginary potential. We identify conventional Friedel oscillations or heavily suppressed density response, respectively.

cond-mat.mes-hall↗

arXiv2021

Dynamics of entanglement after exceptional quantum quench

We investigate a quantum quench from a critical to an exceptional point. The initial state, prepared in the ground state of a critical hermitian system, is time evolved with a non-hermitian SSH model, tuned to its exceptional point. The single particle density matrix exhibits supersonic modes and multiple light cones, characteristic to non-hermitian time evolution. These propagate with integer multiples of the original Fermi velocity. In the long time limit, the fermionic Green's function decays spatially as $1/x^2$, in sharp contrast to the usual $1/x$ decay of non-interacting fermions. The entanglement entropy is understood as if all these supersonic modes arise from independent quasiparticles (though they do not), traveling with the corresponding supersonic light cone velocity. The entropy production rate decreases with time and develops plateaus during the time evolution, signaling the distinct velocities in the propagation of non-local quantum correlations. At late times, the entanglement entropy saturates to a finite value, satisfying a volume law.

cond-mat.str-el↗

arXiv2021

Topologically protected, correlated end spin formation in carbon nanotubes

For most chiralities, semiconducting nanotubes display topologically protected end states of multiple degeneracies. We demonstrate using density matrix renormalization group based quantum chemistry tools that the presence of Coulomb interactions induces the formation of robust end spins. These are the close analogues of ferromagnetic edge states emerging in graphene nanoribbons. The interaction between the two ends is sensitive to the length of the nanotube, its dielectric constant, as well as the size of the end spins: for $S=1/2$ end spins their interaction is antiferromagnetic, while for $S>1/2$ it changes from antiferromagnetic to ferromagnetic as the nanotube length increases. The interaction between end spins can be controlled by changing the dielectric constant of the environment, thereby providing a possible platform for two-spin quantum manipulations.

cond-mat.str-el↗

arXiv2021

Vaporization dynamics of a dissipative quantum liquid

We investigate the stability of a Luttinger liquid, upon suddenly coupling it to a dissipative environment. Within the Lindblad equation, the environment couples to local currents and heats the quantum liquid up to infinite temperatures. The single particle density matrix reveals the fractionalization of fermionic excitations in the spatial correlations by retaining the initial non-integer power law exponents, accompanied by an exponential decay in time with interaction dependent rate. The spectrum of the time evolved density matrix is gapped, which collapses gradually as $-\ln(t)$. The von Neumann entropy crosses over from the early time $-t\ln(t)$ behaviour to $\ln(t)$ growth for late times. The early time dynamics is captured numerically by performing simulations on spinless interacting fermions, using several numerically exact methods. Our results could be tested experimentally in bosonic Luttinger liquids.

cond-mat.str-el↗

arXiv2020

Universal conductance of a PT-symmetric Luttinger liquid after a quantum quench

We study the non-equilibrium dynamics and transport of a PT-symmetric Luttinger liquid (LL) after an interaction quench. The system is prepared in domain wall initial state. After a quantum quench to spatially homogeneous, PT-symmetric LL, the domain wall develops into a flat central region that spreads out ballistically faster than the conventional Lieb-Robinson maximal speed. By evaluating the current inside the regular lightcone, we find a universal conductance $e^2/h$, insensitive to the strength of the PT-symmetric interaction. On the other hand, by repeating the very same time evolution with a hermitian LL Hamiltonian, the conductance is heavily renormalized by the hermitian interaction as $e^2/hK$ with $K$ the LL parameter. Our analytical results are tested numerically, confirming the universality of the conductance in the non-hermitian realm.

cond-mat.str-el↗

arXiv2020

All-electrical spectroscopy of topological phases in semiconductor-superconductor heterostructures

Semiconductors in the proximity of superconductors have been proposed to support phases hosting Majorana bound states. When the systems undergo a topological phase transition towards the Majorana phase, the spectral gap closes, then reopens, and the quasiparticle band spin polarization is inverted. We focus on two paradigmatic semiconductor-superconductor heterostructures and propose an all-electrical spectroscopic probe sensitive to the spin inversion at the topological transition. Our proposal relies on the indirect coupling of a time-dependent electric field to the electronic spin due to the strong Rashba spin-orbit coupling in the semiconductor. We analyze within linear response theory the dynamical correlation functions and demonstrate that some components of the susceptibility can be used to detect the nontrivial topological phases.

cond-mat.mes-hall↗

arXiv2020

Out-of-time-ordered commutators in Dirac--Weyl systems

Quantum information stored in local operators spreads over other degrees of freedom of the system during time evolution, known as scrambling. This process is conveniently characterized by the out-of-time-order commutators (OTOC), whose time dependence reveals salient aspects of the system's dynamics. Here we study the spatially local spin correlation function i.e., the expectation value of spin commutator and the corresponding OTOC of Dirac--Weyl systems in one, two, and three spatial dimensions. The OTOC can be written as the square of the expectation value of the commutator and the variance of the commutator. In principle, the problem features two energy scales, the chemical potential, and the high energy cutoff. We find that only the latter is dominant, therefore the time evolution is separated into only two different regions. The spin correlation function grows linearly with time initially and decays as $t^{-2}$ for late times. The OTOC reveals a universal $t^2$ initial growth from both the commutator and the variance while its late time decay, $t^{-2}$ originates from the variance of the commutator. This late time decay is identified as a characteristic signature or Dirac-Weyl fermions. These features remain present also at finite temperatures. Our results indicate that Dirac--Weyl systems are slow information scramblers and are essential when additional channels for scrambling, i.e., interaction or disorder are analyzed.

cond-mat.mes-hall↗

arXiv2020

Geometrical quench and dynamical quantum phase transition in the $α-T_3$ lattice

We investigate quantum quenches and the Loschmidt echo in the two dimensional, three band $α-T_3$ model, a close descendant of the dice lattice. By adding a chemical potential to the central site, the integral of the Berry curvature of the bands in different valleys is continously tunable by the ratio of the hopping integrals between the sublattices. By investigating one and two filled bands, we find that dynamical quantum phase transition (DQPT), i.e. nonanalytical temporal behaviour in the rate function of the return amplitude, occurs for a certain range of parameters, independent of the band filling. By focusing on the effective low energy description of the model, we find that DQPTs happen not only in the time derivative of the rate function, which is a common feature in two dimensional models, but in the rate function itself. This feature is not related to the change of topological properties of the system during the quench, but rather follows from population inversion for all momenta. This is accompanied by the appearance of dynamical vortices in the time-momentum space of the Pancharatnam geometric phase. The positions of the vortices form an infinite vortex ladder, i.e. a macroscopic phase structure, which allows us to identify the dynamical phases that are separated by the DQPT.

cond-mat.quant-gas↗

arXiv2020

Quantum quench in PT-symmetric Luttinger liquid

A Luttinger liquid (LL) describes low energy excitations of many interacting one dimensional systems, and exhibits universal response both in and out of equilibrium. We analyze its behaviour in the non-hermitian realm after quantum quenching to a PT-symmetric LL by focusing on the fermionic single particle density matrix. For short times, we demonstrate the emergence of unique phenomena, characteristic to non-hermitian systems, that correlations propagate faster than the conventional maximal speed, known as the Lieb-Robinson bound. These emergent supersonic modes travel with velocities that are multiples of the conventional light-cone velocity. This behaviour is argued to be generic for correlators in non-hermitian systems. In the long time limit, we find typical LL behaviour, extending the LL universality to the non-equilibrium non-hermitian case. Our analytical results are benchmarked numerically and indicate that the dispersal of quantum information is much faster in non-hermitian systems.

cond-mat.str-el↗

arXiv2020

Dissipation induced Luttinger liquid correlations in a one dimensional Fermi gas

We study a one-dimensional Fermi gas in the presence of dissipative coupling to environment through the Lindblad equation. The dissipation involves energy exchange with the environment and favours the relaxation of electrons to excitations. After switching on the dissipation, the system approaches a steady state, which is described by a generalized Gibbs ensemble. The fermionic single particle density matrix resembles deceivingly to that in a hermitian interaction quench. It decays inversely with the distance for short times due to the fermionic correlations in the initial state, which changes into a non-integer power law decay for late times, representing dissipation induced Luttinger liquid behaviour. However, the crossover between the two regions occurs due to dissipation induced damping, and is unrelated to the propagation of excitations. The velocity of information spreading is set by the dissipative coupling, and differs significantly from the original sound velocity. The thermodynamic entropy grows as $-t\ln t$ initially, and saturates to an extensive value. Our results can be tested experimentally in one-dimensional Dirac systems.

cond-mat.str-el↗

arXiv2019

Quantum criticality and formation of a singular Fermi liquid in the attractive SU(N > 2) Anderson model

While much is known about repulsive quantum impurity models, significantly less attention has been devoted to their attractive counterparts. This motivated us to study the attractive SU(N) Anderson impurity model. While for the repulsive case, the phase diagram features mild N dependence and the ground state is always a Fermi liquid, in the attractive case a Kosterlitz-Thouless charge localization phase transition is revealed for N > 2. Beyond a critical value of attractive interaction an abrupt jump appears in the number of particles at the impurity site, and a singular Fermi liquid state emerges, where the scattering of quasiparticles is found to exhibit power law behavior with fractional power. The capacity diverges exponentially at the quantum critical point, signaling the Kosterlitz-Thouless transition.

cond-mat.mes-hall↗

arXiv2019

Collective modes for helical edge state interacting with quantum light

We investigate the light-matter interaction between the edge state of a 2D topological insulator and quantum electromagnetic field. The interaction originates from the Zeeman term between the spin of the edge electrons and the magnetic field, and also through the Peierls substition. The continuous U(1) symmetry of the system in the absence of the vector potential reduces into discrete time reversal symmetry in the presence of the vector potential. Due to light-matter interaction, a superradiant ground state emerges with spontaneously broken time reversal symmetry, accompanied by a net photocurrent along the edge, generated by the vector potential of the quantum light. The spectral function of the photon field reveals polariton continuum excitations above a threshold energy, corresponding to a Higgs mode and another low energy collective mode due to the phase fluctuations of the ground state. This collective mode is a zero energy Goldstone mode that arises from the broken continuous U(1) symmetry in the absence of the vector potential, and acquires finite a gap in the presence of the vector potential. The optical conductivity of the edge electrons is calculated using the random phase approximation by taking the fluctuation of the order parameter into account. It contains the collective modes as a Drude peak with renormalized effective mass, which moves to finite frequencies as the symmetry of the system is lowered by the inclusion of the vector potential.

cond-mat.str-el↗

arXiv2019

The Kibble-Zurek mechanism at exceptional points

Exceptional points (EPs) are ubiquitous in non-hermitian systems, and represent the complex counterpart of critical points. By driving a system through a critical point at finite rate induces defects, described by the Kibble-Zurek mechanism, which finds applications in diverse fields of physics. Here we generalize this to a ramp across an EP. We find that adiabatic time evolution brings the system into an eigenstate of the final non-hermitian Hamiltonian and demonstrate that for a variety of drives through an EP, the defect density scales as $τ^{-(d+z)ν/(zν+1)}$ in terms of the usual critical exponents and $1/τ$ the speed of the drive. Defect production is suppressed compared to the conventional hermitian case as the defect state can decay back to the ground state close to the EP. We provide a physical picture for the studied dynamics through a mapping onto a Lindblad master equation with an additionally imposed continuous measurement.

cond-mat.str-el↗

arXiv2019

Optimal protocols for finite-duration quantum quenches in the Luttinger model

Reaching a target quantum state from an initial state within a finite temporal window is a challenging problem due to non-adiabaticity. We study the optimal protocol for swithcing on interactions to reach the ground state of a weakly interacting Luttinger liquid within a finite time $τ$, starting from the non-interacting ground state. The protocol is optimized by minimizing the excess energy at the end of the quench, or by maximizing the overlap with the interacting ground state. We find that the optimal protocol is symmetric with respect to $τ/2$, and can be expressed as a functional of the occupation numbers of the bosonic modes in the final state. For short quench durations, the optimal protocol exhibits fast oscillation and excites high energy modes. In the limit of large $τ$, minimizing energy requires a smooth protocol while maximizing overlap requires a linear quench protocol. In this limit, the minimal energy and maximal overlap are both universal functions of the system size and the duration of the protocol.

cond-mat.str-el↗