arXiv subjects

Natan Andrei

Publications and source records attributed to Natan Andrei.

At least 37 records · Page 2Linked to original sources

arXiv2024

Edge Spin fractionalization in one-dimensional spin-$S$ quantum antiferromagnets

We show that a gapped spin-$S$ chain with antiferromagnetic (AFM) order exhibits in the thermodynamic limit exponentially localized fractional $\pm \frac{S}{2}$ edge modes when the system possesses U(1) symmetry. We show this for integrable and non integrable spin chains both analytically and numerically. Through exact analytical solutions, we show that an AFM spin-$\frac{1}{2}$ chain with {\it explicitly} broken $\mathbb{Z}_2$ symmetry and an integrable AFM spin-$1$ chain with {\it spontaneously} broken $\mathbb{Z}_2$ symmetry have $\pm \frac{1}{4}$ and $\pm \frac{1}{2}$ fractionalized edge modes, respectively. Furthermore, employing the density matrix renormalization group technique, we extend this analysis to {\it generic} $XXZ-S$ chains with $S\leq 3$ and demonstrate that these fractional spins are robust quantum observables, substantiated by the observation of a variance of the associated fractional spin operators that is consistent with a vanishing functional form in the thermodynamic limit. Moreover, we find that the edge modes are robust to disorder that couples to the Néel order parameter.

cond-mat.str-el↗

arXiv2024

A spin chain with non-Hermitian $\mathscr{PT}-$symmetric boundary couplings: exact solution, dissipative Kondo effect, and phase transitions on the edge

We construct an exactly solvable $\mathscr{PT}-$symmetric non-Hermitian model where a spin$-\frac{1}{2}$ isotropic quantum Heisenberg spin chain is coupled to two spin$-\frac{1}{2}$ Kondo impurities at its boundaries with coupling strengths that are complex conjugates of each other. Solving the model by means of a combination of the Bethe Ansatz and density matrix renormalization group (DMRG) techniques, we show that the model exhibits three distinct boundary phases: a $\mathscr{PT}$ symmetric phase with a dissipative Kondo effect, a phase with bound modes and spontaneously broken $\mathscr{PT}$ symmetry, and a phase with an effectively unscreened spin (i.e. a free local moment). In the Kondo and the unscreened phases, the $\mathscr{PT}-$symmetry is unbroken, and hence all states have real energies, whereas in the bound mode phases, in addition to the states with real energies, there exist states with complex energy eigenvalues that appear in complex conjugate pairs, signaling spontaneous breaking of the $\mathscr{PT}-$symmetry. The exact solution is used to provide an accessible benchmark for DMRG with a non-Hermitian matrix product operator representation that demonstrates an accuracy comparable to its Hermitian limit thus showing the power of DMRG to handle non-Hermitian many body calculations.

cond-mat.str-el↗

arXiv2024

The Kondo effect in the quantum $XX$ spin chain

We investigate the boundary phenomena that arise in a finite-size $XX$ spin chain interacting through an $XX$ interaction with a spin$-\frac{1}{2}$ impurity located at its edge. Upon Jordan-Wigner transformation, the model is described by a quadratic Fermionic Hamiltonian. Our work displays, within this ostensibly simple model, the emergence of the Kondo effect, a quintessential hallmark of strongly correlated physics. We also show how the Kondo cloud shrinks and turns into a single particle bound state as the impurity coupling increases beyond a critical value. Using both \textit{Bethe Ansatz} and \textit{exact diagonalization} techniques, we show that the local moment of the impurity is screened by different mechanisms depending on the ratio of the boundary and bulk coupling. When the ratio falls below the critical value $\sqrt{2}$, the impurity is screened via the multiparticle Kondo effect. However, when the ratio between the coupling exceeds the critical value , a bound mode is formed at the impurity site which screens the spin of the impurity. We show that the boundary phase transition is reflected in local ground state properties by calculating the spinon density of states, the magnetization at the impurity site in the presence of a global magnetic field, and the finite temperature susceptibility. We find that the spinon density of states in the Kondo phase has the characteristic Lorentzian peak that moves from the Fermi level to the maximum energy of the spinon as the impurity coupling is increased and becomes a localized bound mode in the bound mode phase. Moreover, the impurity magnetization and the finite temperature impurity susceptibility behave differently in the two phases. When the boundary coupling $J_{\mathrm{imp}}$ exceeds the critical value $\sqrt{2}J$, the model is no longer boundary conformal invariant as a massive bound mode appears at the impurity site.

cond-mat.str-el↗

arXiv2023

Spin fractionalization and zero modes in the spin-$\frac{1}{2}$ XXZ chain with boundary fields

In this work we argue that the antiferromagnetic spin $\frac{1}{2}$ XXZ chain in the gapped phase with boundary magnetic fields hosts fractional spin $\frac{1}{4}$ at its edges. Using a combination of Bethe ansatz and the density matrix renormalization group we show that these fractional spins are sharp quantum observables in both the ground and the first excited state as the associated fractional spin operators have zero variance. In the limit of zero edge fields, we argue that these fractional spin operators once projected onto the low energy subspace spanned by the ground state and the first excited state, identify with the strong zero energy mode discovered by P. Fendley \cite{Fendley}.

cond-mat.str-el↗

arXiv2023

Kondo effect in the isotropic Heisenberg spin chain

We investigate the boundary effects that arise when spin-$\frac{1}{2}$ impurities interact with the edges of the antiferromagnetic spin-$\frac{1}{2}$ Heisenberg chain through spin exchange interactions. We consider both cases when the couplings are ferromagnetic or anti-ferromagnetic. We find that in the case of antiferromagnetic interaction, when the impurity coupling strength is much weaker than that in the bulk, the impurity is screened in the ground state via the Kondo effect. The Kondo phase is characterized by the Lorentzian density of states and dynamically generated Kondo temperature $T_K$. As the impurity coupling strength increases, $T_K$ increases until it reaches its maximum value $T_0=2πJ$ which is the maximum energy carried by a single spinon. When the impurity coupling strength is increased further, we enter another phase, the bound mode phase, where the impurity is screened in the ground state by a single particle bound mode exponentially localized at the edge to which the impurity is coupled. We find that the impurity can be unscreened by removing the bound mode. There exists a boundary eigenstate phase transition between the Kondo and the bound-mode phases, a transition which is characterized by the change in the number of towers of the Hilbert space. The transition also manifests itself in ground state quantities like local impurity density of states and the local impurity magnetization. When the impurity coupling is ferromagnetic, the impurity is unscreened in the ground state; however, when the absolute value of the ratio of the impurity and bulk coupling strengths is greater than $\frac{4}{5}$, the impurity can be screened by adding a bound mode that costs energy greater than $T_0$. When two impurities are considered, the phases exhibited by each impurity remain unchanged in the thermodynamic limit, but nevertheless the system exhibits a rich phase diagram.

cond-mat.str-el↗

arXiv2022

Boundary Quantum Phase Transitions in the Spin $\frac{1}{2}$ Heisenberg Chain with Boundary Magnetic Fields

We consider the spin $\frac{1}{2}$ Heisenberg chain with boundary magnetic fields and analyze it using a combination of Bethe ansatz and density matrix renormalization group (DMRG) techniques. We show that the system exhibits several different ground states which depend on the orientation of the boundary magnetic fields. When both the boundary fields take equal values greater than a critical field strength, each edge in the ground state accumulates a fractional spin which saturates to spin $\frac{1}{4}$, which is similar to systems exhibiting symmetry protected topological phases (SPT). Unlike in SPT systems, the fractional boundary spin in the Heisenberg spin chain is not a genuine quantum number since the variance of the associated operator does not vanish, this is due to the absence of a bulk gap. The system exhibits high energy bound states when the boundary fields take values greater than the critical field. All the excitations in the system can be sorted out into towers whose number depends on the number of bound states exhibited by the system. As the boundary fields are varied, in addition to the ground state phase transition, we find that the system may undergo an eigenstate phase transition (EPT) where the number of towers of the Hilbert space changes. We further inquire how the EPT reflects itself on local ground state properties by computing the magnetization profile $\langle S^z_j \rangle$ using DMRG. We identify a clear qualitative change from low edge fields to high edge fields when crossing the critical field. We though are unable to conclude on the basis of our data that EPT corresponds to a genuine phase transition in the ground state.

cond-mat.str-el↗

arXiv2021

Rise and fall of Yu-Shiba-Rusinov bound-states in charge conserving $s$-wave one-dimensional superconductors

We re-examine the problem of a magnetic impurity coupled to a superconductor focusing on the role of quantum fluctuations. We study in detail, a system that consists of a one-dimensional charge conserving spin-singlet superconductor coupled to a boundary magnetic impurity. Our main finding is that quantum fluctuations lead to the destruction of Yu-Shiba-Rusinov (YSR) intra-gap bound-states in all but a narrow region of the phase diagram. We carry out our analysis in three stages, increasing the role of the quantum fluctuations at each stage. First we consider the limit of a classical impurity and study the bulk semiclassically, finding YSR states throughout the phase diagram, a situation similar to conventional BCS superconductors. In the second stage, we reintroduce quantum fluctuations in the bulk and find that the YSR state is suppressed over half of the phase diagram, existing only around the quantum critical point separating the unscreened and the partially screened phases. In the final stage we solve exactly the full interacting model with arbitrary coupling constants using Bethe Ansatz. We find that including both the quantum fluctuating bulk and quantum impurity destabilizes the YSR state over most of the phase diagram allowing it to exist only in a small region, the YSR regime, between a Kondo-screened and an unscreened regime. Within the YSR regime a first order phase transition occurs between a spin singlet and doublet ground state. We also find that for large enough impurity spin exchange interaction a renormalized Kondo-screened regime is established. In this regime, not found for BCS superconductors, there is no YSR state and a renormalized Kondo temperature scale is generated.

cond-mat.str-el↗

arXiv2021

Multi-particle quantum walks and Fisher information in one-dimensional lattices

Recent experiments on quantum walks (QWs) of a single and two particles demonstrated subtle quantum statistics-dependent walks in one-dimensional (1D) lattices. However the roles of interaction and quantum statistics in such a kind of walks are little known at a many-body level. In this letter, using time-evolving block decimation algorithm and many-body perturbation theory we rigorously study QWs, Bloch oscillations and quantum Fisher informations (FIs) for three indistinguishable bosons and fermions in 1D lattices. We show that such strongly correlated many-body QWs not only give rise to statistics-and-interaction-dependent ballistic transports of scattering states, two- and three-body bound states, but also present a quantum enhanced precision measurement of the gravitational force. It turns out that in contrast to the walks of the fermions, the QWs of three bosons exhibit richer dynamics of co-walkings and competitive Bloch oscillations, which remarkably present a surprising time scaling $t^3$ of FI below a characteristic time $t_0$ and saturate to the fundamental limit of $t^2$ for $t>t_0$.

cond-mat.quant-gas↗

arXiv2021

Many-body wavefunctions for quantum impurities out of equilibrium. I. The nonequilibrium Kondo model

We present here the details of a method [A. B. Culver and N. Andrei, Phys. Rev. B 103, L201103 (2021)] for calculating the time-dependent many-body wavefunction that follows a local quench. We apply the method to the voltage-driven nonequilibrium Kondo model to find the exact time-evolving wavefunction following a quench where the dot is suddenly attached to the leads at $t=0$. The method, which does not use Bethe ansatz, also works in other quantum impurity models and may be of wider applicability. We show that the long-time limit (with the system size taken to infinity first) of the time-evolving wavefunction of the Kondo model is a current-carrying nonequilibrium steady state that satisfies the Lippmann-Schwinger equation. We show that the electric current in the time-evolving wavefunction is given by a series expression that can be expanded either in weak coupling or in strong coupling, converging to all orders in the steady-state limit in either case. The series agrees to leading order with known results in the well-studied regime of weak antiferromagnetic coupling and also reveals a universal regime of strong ferromagnetic coupling with Kondo temperature $T_K^{(F)} = D e^{-\frac{3π^2}{8} ρ|J|}$ ($J<0$, $ρ|J|\to\infty$). In this regime, the differential conductance $dI/dV$ reaches the unitarity limit $2e^2/h$ asymptotically at large voltage or temperature.

cond-mat.str-el↗

arXiv2021

Many-body wavefunctions for quantum impurities out of equilibrium. II. Charge fluctuations

We extend the general formalism discussed in the previous paper [A. B. Culver and N. Andrei, Phys. Rev. B 103, 195106 (2021)] to two models with charge fluctuations: the interacting resonant level model and the Anderson impurity model. In the interacting resonant level model, we find the exact time-evolving wavefunction and calculate the steady state impurity occupancy to leading order in the interaction. In the Anderson impurity model, we find the nonequilibrium steady state for small or large Coulomb repulsion $U$, and we find that the steady state current to leading order in $U$ agrees with a Keldysh perturbation theory calculation.

cond-mat.str-el↗

arXiv2021

Many-body wavefunctions for quantum impurities out of equilibrium

We present a method for calculating the time-dependent many-body wavefunction that follows a local quench. We apply the method to the voltage-driven nonequilibrium Kondo model to find the exact time-evolving wavefunction following a quench where the dot is suddenly attached to the leads at $t=0$. The method, which does not use Bethe ansatz, also works in other quantum impurity models (we include results for the interacting resonant level and the Anderson impurity model) and may be of wider applicability. In the particular case of the Kondo model, we show that the long-time limit (with the system size taken to infinity first) of the time-evolving wavefunction is a current-carrying nonequilibrium steady state that satisfies the Lippmann-Schwinger equation. We show that the electric current in the time-evolving wavefunction is given by a series expression that can be expanded either in weak coupling or in strong coupling, converging to all orders in the steady-state limit in either case. The series agrees to leading order with known results in the well-studied regime of weak antiferromagnetic coupling and also reveals another universal regime of strong ferromagnetic coupling, with Kondo temperature $T_K^{(F)} = D e^{-\frac{3π^2}{8} ρ|J|}$ ($J<0$, $ρ|J|\to\infty$). In this regime, the differential conductance $dI/dV$ reaches the unitarity limit $2e^2/h$ asymptotically at large voltage or temperature.

cond-mat.str-el↗

arXiv2021

Boundary-Induced Topological and Mid-Gap States in Charge Conserving One-Dimensional Superconductors

We investigate one-dimensional charge conserving, spin-singlet (SSS) and spin-triplet (STS) superconductors in the presence of boundary fields. In systems with Open Boundary Conditions (OBC) it has been demonstrated that STS display a four-fold topological degeneracy, protected by the $\mathbb{Z}_2$ symmetry which reverses the spins of all fermions, whereas SSS are topologically trivial. In this work we show that it is not only the type of the bulk superconducting instability that determines the eventual topological nature of a phase, but rather the interplay between bulk and boundary properties. In particular we show by means of the Bethe Ansatz technique that SSS may as well be in a $\mathbb{Z}_2$-protected topological phase provided suitable "twisted" open boundary conditions ${\widehat{OBC}}$ are imposed. More generally, we find that depending on the boundary fields, a given superconductor, either SSS or STS, may exhibits several types of phases such as topological, mid-gap and trivial phases; each phase being characterized by a boundary fixed point which which we determine. Of particular interest are the mid-gap phases which are stabilized close to the topological fixed point. They include both fractionalized phases where spin-$\frac{1}{4}$ bound-states are localized at the two edges of the system and un-fractionalized phases where a spin-$\frac{1}{2}$ bound-state is localized at either the left or the right edge.

cond-mat.supr-con↗

arXiv2020

Nonperturbative approach to quench dynamics. II. Universal electric current of the nonequilibrium Kondo model

In the previous paper, we found a series expression for the average electric current following a quench in the nonequilibrium Kondo model driven by a bias voltage. Here, we evaluate the steady state current in the regimes of strong and weak coupling. We obtain the standard leading order results in the usual weak antiferromagnetic regime, and we also find a new universal regime of strong ferromagnetic coupling with Kondo temperature $T_K = D e^{\frac{3π^2}{8} ρJ}$. In this regime, the differential conductance $dI/dV$ reaches the unitarity limit $2e^2/h$ asymptotically at large voltage or temperature.

cond-mat.str-el↗

arXiv2020

Edge Modes in One Dimensional Topological Charge Conserving Spin-Triplet Superconductors: Exact Results from Bethe Ansatz

Charge conserving spin singlet and spin triplet superconductors in one dimension are described by the $U(1)$ symmetric Thirring Hamiltonian. We solve the model with open boundary conditions on the a finite line segment by means of the Bethe Ansatz. We show that the ground state displays a fourfold degeneracy when the bulk is in the spin triplet superconducting phase. This degeneracy corresponds to the existence of zero energy boundary bound states localized at the edges which may be interpreted, in the light of the previous semi-classical analysis due to Kesselman and Berg \cite{Keselman2015}, as resulting from the existence of fractional spin $\pm 1/4$ localized at the two edges of the system.

cond-mat.str-el↗

arXiv2020

Quantum Dot at a Luttinger liquid edge

We study a system consisting of a Luttinger liquid coupled to a quantum dot on the boundary. The Luttinger liquid is expressed in terms of fermions interacting via density-density coupling and the dot is modeled as an interacting resonant level on to which the bulk fermions can tunnel. We solve the Hamiltonian exactly and construct all eigenstates. We study both the zero and finite temperature properties of the system, in particular we compute the exact dot occupation as a function of the dot energy in all parameter regimes. The system is seen to flow from weak to to strong coupling for all values of the bulk interaction, with the flow characterized by a non-perturbative Kondo scale. We identify the critical exponents at the weak and strong coupling regimes.

cond-mat.str-el↗

arXiv2019

Kondo impurity at the edge of a superconducting wire

Quantum impurity models are prevalent throughout many body physics, providing some prime examples of strongly correlated systems. Aside from being of great interest in themselves they can provide deep insight into the effects of strong correlations in general. The classic example is the Kondo model wherein a magnetic impurity is screened at low energies by a non interacting metallic bath. Here we consider a magnetic impurity coupled to a quantum wire with pairing interaction which dynamically generates a mass gap. Using Bethe Ansatz we solve the system exactly finding that it exhibits both screened and unscreened phases for an antiferromagnetic impurity. We determine the ground state density of states and magnetization in both phases as well as the excitations. In contrast to the well studied case of magnetic impurities in superconductors we find that there are no intragap bound states in the spectrum. The phase transition is not associated to a level crossing but with quantum fluctuations.

cond-mat.str-el↗

arXiv2019

Non-equilibrium aspects of integrable models

Driven by breakthroughs in experimental and theoretical techniques, the study of non-equilibrium quantum physics is a rapidly expanding field with many exciting new developments. Amongst the manifold ways the topic can be investigated, one dimensional system provide a particularly fine platform. The trifecta of strongly correlated physics, powerful theoretical techniques and experimental viability have resulted in a flurry of research activity over the last decade or so. In this review we explore the non equilibrium aspects of one dimensional systems which are integrable. Through a number of illustrative examples we discuss non equilibrium phenomena which arise in such models, the role played by integrability and the consequences these have for more generic systems.

cond-mat.quant-gas↗

arXiv2019

Quantum Work of an Optical Lattice

A classic example of a quantum quench concerns the release of a interacting Bose gas from an optical lattice. The local properties of quenches such as this have been extensively studied however the global properties of these non-equilibrium quantum systems have received far less attention. Here we study several aspects of global non-equilibrium behavior by calculating the amount of work done by the quench as measured through the work distribution function. Using Bethe Ansatz techniques we determine the Loschmidt amplitude and work distribution function of the Lieb-Liniger gas after it is released from an optical lattice. We find the average work and its universal edge exponents from which we determine the long time decay of the Loshcmidt echo and highlight striking differences caused by the the interactions as well as changes in the geometry of the system. We extend our calculation to the attractive regime of the model and show that the system exhibits properties similar to the super Tonks-Girardaeu gas. Finally we examine the prominent role played by bound states in the work distribution and show that, with low probability, they allow for work to be extracted from the quench.

cond-mat.str-el↗