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Natan Andrei

Publications and source records attributed to Natan Andrei.

At least 55 records · Page 3Linked to original sources
arXiv2019

Quantum impurity in a Luttinger liquid: Exact solution of the Kane-Fisher model

A Luttinger Liquid coupled to a quantum impurity describes a large number of physical systems. The Hamiltonian consists of left- and right-moving fermions interacting among themselves via a density-density coupling and scattering off a localised transmitting and reflecting impurity. We solve exactly the Hamiltonian by means of an incoming-outgoing scattering Bethe basis which properly incorporates all scattering processes. A related model, the Weak-Tunnelling model, wherein the impurity is replaced by a tunnel junction, is solved by the same method. The consistency of the construction is established through a generalised Yang-Baxter relation. Periodic boundary conditions are imposed and the resulting Bethe Ansatz equations are derived by means of the Off Diagonal Bethe Ansatz approach. We derive the spectrum of the model for all coupling constant regimes and calculate the impurity free energy. We discuss the low energy behaviour of the systems for both repulsive and attractive interactions.

cond-mat.str-el↗
arXiv2019

Loschmidt Amplitude and Work Distribution in Quenches of the Sine-Gordon Model

The Sine-Gordon - equivalently, the massive Thirring - Hamiltonian is ubiquitous in low-dimensional physics, with applications that range from cold atom and strongly correlated systems to quantum impurities. We study here its non-equilibrium dynamics using the quantum quench protocol - following the system as it evolves under the Sine-Gordon Hamiltonian from initial Mott type states with large potential barriers. By means of the Bethe Ansatz we calculate exactly the Loschmidt amplitude, the fidelity and work distribution characterizing these quenches for different values of the interaction strength. Some universal features are noted as well as an interesting duality relating quenches in different parameter regimes of the model.

cond-mat.str-el↗
arXiv2018

Simplified Thermodynamics for Quantum Impurity Models

Quantum impurity models play an important role in many areas of physics from condensed matter to AMO and quantum information. They are important models for many physical systems but also provide key insights to understanding much more complicated scenarios. In this paper we introduce a simplified method to describe the thermodynamic properties of integrable quantum impurity models. We show this method explicitly using the anisotropic Kondo and the interacting resonant level models. We derive a simplified expression for the free energy of both models in terms of a single physically transparent integral equation which is valid at all temperatures and values of the coupling constants.

cond-mat.str-el↗
arXiv2018

Quench Dynamics of the Gaudin-Yang Model

We study the quench dynamics of one dimensional bosons or fermion quantum gases with either attractive or repulsive contact interactions. Such systems are well described by the Gaudin-Yang model which turns out to be quantum integrable. We use a contour integral approach, the Yudson approach, to expand initial states in terms of Bethe Ansatz eigenstates of the Hamiltonian. Making use of the contour, we obtain a complete set of eigenstates, including both free states and bound states. These states constitute a larger Hilbert space than described by the standard String hypothesis. We calculate the density and noise correlations of several quenched systems such as a static or kinetic impurity evolving in an array of particles.

cond-mat.quant-gas↗
arXiv2018

Quantum Dot in Interacting Environments

A quantum impurity attached to an interacting quantum wire gives rise to an array of of new phenomena. Using Bethe Ansatz we solve exactly models describing two geometries of a quantum dot coupled to an interacting quantum wire: a quantum dot that is (i) side-coupled and (ii) embedded in a Luttinger liquid. We find the eigenstates and determine the spectrum through the Bethe Ansatz equations. Using this we derive exact expressions for the ground state dot occupation. The thermodynamics are then studied using the thermodynamics Bethe Ansatz equations. It is shown that at low energies the dot becomes fully hybridized and acts as a backscattering impurity or tunnel junction depending on the geometry and furthermore that the two geometries are related by changing the sign of the interactions. Although remaining strongly coupled for all values of the interaction in the wire, there exists competition between the tunneling and backscattering leading to a suppression or enhancement of the dot occupation depending on the sign of the bulk interactions.

cond-mat.str-el↗
arXiv2016

Quench dynamics in integrable systems

These notes cover in some detail lectures I gave at the Les Houches Summer School 2012. I describe here work done with Deepak Iyer with important contributions from Hujie Guan. I discuss some aspects of the physics revealed by quantum quenches and present a formalism for studying the quench dynamics of integrable systems. The formalism presented generalizes an approach by Yudson and is applied to Lieb-Liniger model which describes a gas of $N$ interacting bosons moving on the continuous infinite line while interacting via a short range potential. We carry out the quench from several initial states and for any number of particles and compute the evolution of the density and the noise correlations. In the long time limit the system dilutes and we find that for any value of repulsive coupling independently of the initial state the system asymptotes towards astrongly repulsive gas, while for any value of attractive coupling, the system forms a maximal bound state that dominates at longer times. In either case the system equilibrates but does not thermalize, an effect that is consistent with prethermalization. These results can be confronted with experiments. For much more detail see: Phys. Rev. A 87, 053628 (2013) on which these notes are based. Further applications of the approach to the Heisenberg model and to the Anderson model will be presented elsewhere.

cond-mat.quant-gas↗
arXiv2016

Failure of the GGE hypothesis for integrable models with bound states

In this work we study the applicability of the GGE to integrable one dimensional systems with bound states. We find that the GGE fails to describe the long time dynamics for most initial states including eigenstates. We present our calculations studying the attractive Lieb-Liniger gas and the XXZ magnet, though similar results may be obtained for other models.

cond-mat.quant-gas↗
arXiv2015

Correlation functions of the Lieb-Liniger gas and the LeClair-Mussardo formula

In this letter we derive formulas for multi point correlation functions, in the thermodynamic limit, for the Lieb Liniger gas taken with respect to arbitrary eigenstates. These results apply for the ground state, thermal states and GGE states. We obtain these correlation functions as a series of multiple integrals of progressively higher dimensions. These integrals converge rapidly for short distance correlation functions and low densities of particles. The series derived matches exactly the LeClair Mussardo formula for correlation functions of relativistic integrable models.

cond-mat.quant-gas↗
arXiv2015

Equilibration and GGE for hard wall boundary conditions

In this work we present an analysis of a quench for the repulsive Lieb-Liniger gas confined to a large box with hard wall boundary conditions. We study the time average of local correlation functions and show that both the quench action approach and the GGE formalism are applicable for the long time average of local correlation functions. We find that the time average of the system corresponds to an eigenstate of the Lieb-Liniger Hamiltonian and that this eigenstate is related to an eigenstate of a Lieb-Liniger Hamiltonian with periodic boundary conditions on an interval of twice the length and with twice as many particles (a doubled system). We further show that local operators with support far away from the boundaries of the hard wall have the same expectation values with respect to this eigenstate as corresponding operators for the doubled system. We present an example of a quench where the gas is initially confined in several moving traps and then released into a bigger container, an approximate description of the Newton cradle experiment. We calculate the time average of various correlation functions for long times after the quench.

cond-mat.quant-gas↗
arXiv2014

Statistics-dependent quantum co-walking of two particles in one-dimensional lattices with nearest-neighbor interactions

We investigate continuous-time quantum walks of two indistinguishable particles [bosons, fermions or hard-core bosons (HCBs)] in one-dimensional lattices with nearest-neighbor interactions. The results for two HCBs are well consistent with the recent experimental observation of two-magnon dynamics [Nature 502, 76 (2013)]. The two interacting particles can undergo independent- and/or co-walking depending on both quantum statistics and interaction strength. Two strongly interacting particles may form a bound state and then co-walk like a single composite particle with statistics-dependent walk speed. Analytical solutions for the scattering and bound states, which appear in the two-particle quantum walks, are obtained by solving the eigenvalue problem in the two-particle Hilbert space. In the context of degenerate perturbation theory, an effective single-particle model for the quantum co-walking is analytically derived and the walk seep of bosons is found to be exactly three times of the ones of fermions/HCBs. Our result paves the way for experimentally exploring quantum statistics via two-particle quantum walks.

quant-ph↗
arXiv2014

Stron eigenstate thermalization hypothesis

We present a generalization of the ETH conjecture. Using this generalization we are able to derive the fact that an arbitrary eigenstate of a general many body system may be used to represent microcanonical ensemble in any many body experiment that involves only local operators and projectors onto eigenstates of the system Hamiltonian. In particular we extend the ETH to include some non-local operators. We present a derivation of this conjecture in the case of a many body model whose Hamiltonian is composed of two parts: an integrable Hamiltonian and a small but finite Gaussian perturbation.

cond-mat.stat-mech↗
arXiv2014

Time Evolution of Superradiance

The superradiant behaviour of the Dicke model is examined using the Yudson representation. This is achieved by computing the time evolution of the mean photon current density and photon number. Extensions of this model including energy splitting and spatial separation are then investigated using this technique.

physics.optics↗
arXiv2014

How to experimentally detect a GGE? - Universal Spectroscopic Signatures of the GGE in the Tonks gas

In this work we study the properties of the density density correlation function of the 1-D Lieb-Liniger model with infinite repulsion in the GGE regime. The GGE describes the equilibrated system in the long time limit after a quench from a generic initial state. In the case that the initial and hence the final state has low entropy per particle we find that the density density correlation function has a universal form, in particular it depends on a few parameters corresponding to "key" momenta and has power law dependence on the distance. This provides an experimental signature of the GGE which may readily be identified through spectroscopy. These signatures are universal and robust to initial sate preparation.

cond-mat.quant-gas↗
arXiv2014

Equilibration and Generalized GGE in the Lieb Liniger gas

We study the nonequilibrium properties of the one dimensional Lieb Liniger model in the finite repulsion regime. Introducing a new version of the Yudson representation applicable to finite size systems and appropriately taking the infinite volume limit we are able to study equilibration of the Lieb Liniger gas in the thermodynamic limit. We provide a formalism to compute various correlation functions for highly non equilibrium initial states. We are able to find explicit analytic expressions for the long time limit of the expectation of the density, density density and related correlation functions. We show that the gas equilibriates to a diagonal ensemble which we show is equivalent to a generalized version of the GGE for sufficiently simple correlation functions, which in particular include density correlations.

cond-mat.quant-gas↗
arXiv2014

Quantum Walks of Two Interacting Particles in One Dimension

We investigate continuous-time quantum walks of two indistinguishable particles (bosons, fermions or hard-core bosons) in one-dimensional lattices with nearest-neighbour interactions. The two interacting particles can undergo independent- and/or co-walking dependent on both quantum statistics and interaction strength. We find that two strongly interacting particles may form a bound state and then co-walk like a single composite particle with statistics-dependent propagation speed. Such an effective single-particle picture of co-walking is analytically derived in the context of degenerate perturbation and the analytical results are well consistent with direct numerical simulation. In addition to implementing universal quantum computation and observing bound states, two-particle quantum walks offer a novel route to detecting quantum statistics. Our theoretical results can be examined in experiments of light propagations in two-dimensional waveguide arrays or spin-impurity dynamics of ultracold atoms in one-dimensional optical lattices.

quant-ph↗
arXiv2014

Single-molecule-mediated heat current between an electronic and a bosonic bath

In molecular devices electronic degrees of freedom are coupled to vibrational modes of the molecule, offering an opportunity to study fundamental aspects of this coupling between at the nanoscale. To this end we consider the nonequilibrium heat exchange between a conduction band and a bosonic bath mediated by a single molecule. For molecules large enough so that on-site interactions can be dropped we carry out an asymptotically exact calculation of the heat current, governed by the smallness of the electron-phonon coupling, and obtain the steady state heat current driven by a finite temperature drop. At low temperatures the heat current is found to have a power-law behavior with respect to the temperature difference with the power depending on the nature of the bosonic bath. At high temperatures, on the other hand, the current is linear in the temperature difference for all types of bosonic baths. The crossover between these behaviors is described. Some of the results are given a physical explanation by comparing to a perturbative Master equation calculation (whose limitation we examine).

cond-mat.str-el↗
arXiv2013

Quench Dynamics of the Anisotropic Heisenberg Model

We develop an analytic approach for the study of the quench dynamics of the anisotropic Heisenberg model (XXZ model) on the infinite line. We present the exact time-dependent wavefunctions after a quench in an integral form for any initial state and for any anisotropy $Δ$ by means of a generalized Yudson contour representation. We calculate the evolution of several observables from two particular initial states: starting with a local Nèel state we calculate the time evolution of the antiferromagnetic order parameter--staggered magnetization; starting with a state with consecutive flipped spins we calculate the propagation of magnons and bound state excitations, and the induced spin currents. We also show how the "string" solution of Bethe Ansatz equations emerge naturally from the contour approach. We confront our results with experiments and numerical methods where possible.

cond-mat.quant-gas↗