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Natan Andrei

Publications and source records attributed to Natan Andrei.

At least 73 records · Page 4Linked to original sources
arXiv2013

An exact formalism for the quench dynamics of integrable models

We describe a formulation for studying the quench dynamics of integrable systems generalizing an approach by Yudson. We study the evolution of the Lieb-Liniger model, a gas of interacting bosons moving on the continuous infinite line and interacting via a short range potential. The formalism allows us to quench the system from any initial state. We find that for any value of repulsive coupling independently of the initial state the system asymptotes towards a strongly 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. We compare this to quenches in a Bose-Hubbard lattice and show that there, initial states determine long-time dynamics independent of the sign of the coupling.

cond-mat.quant-gas↗
arXiv2012

Quench dynamics of the interacting Bose gas in one dimension

We obtain an exact expression for the time evolution of the interacting Bose gas following a quench from a generic initial state using the Yudson representation for integrable systems. We study the time evolution of the density and noise correlation for a small number of bosons and their asymptotic behavior for any number. We show that for any value of the coupling, as long as it is repulsive, the system asymptotes towards a strongly repulsive gas, while for any value of an attractive coupling the long time behavior is dominated by the maximal bound state. This occurs independently of the initial state and can be viewed as an emerging "dynamic universality".

cond-mat.quant-gas↗
arXiv2011

Quantum quenches and driven dynamics in a single-molecule device

The nonequilibrium dynamics of molecular devices is studied in the framework of a generic model for single-molecule transistors: a resonant level coupled by displacement to a single vibrational mode. In the limit of a broad level and in the vicinity of the resonance, the model can be controllably reduced to a form quadratic in bosonic operators, which in turn is exactly solvable. The response of the system to a broad class of sudden quenches and ac drives is thus computed in a nonperturbative manner, providing an asymptotically exact solution in the limit of weak electron-phonon coupling. From the analytic solution we are able to (1) explicitly show that the system thermalizes following a local quantum quench, (2) analyze in detail the time scales involved, (3) show that the relaxation time in response to a quantum quench depends on the observable in question, and (4) reveal how the amplitude of long-time oscillations evolves as the frequency of an ac drive is tuned across the resonance frequency. Explicit analytical expressions are given for all physical quantities and all nonequilibrium scenarios under study.

cond-mat.str-el↗
arXiv2007

Strong-to-weak-coupling duality in the nonequilibrium interacting resonant-level model

A strong-to-weak-coupling duality is established for the nonequilibrium interacting resonant-level model, describing tunneling through a single spinless level, capacitively coupled to two leads by a contact interaction. For large capacitive coupling, U, and in the presence of a finite voltage bias, the model maps onto an equivalent model with a small capacitive coupling ρU' \sim 1/ ρU. Here ρis the conduction-electron density of states. This duality is generic to all high-energy cutoff schemes, however its details may vary from one regularization scheme to another. In particular, it has the status of an exact mapping within Abelian bosonization, applicable to all repulsive interactions whether weak, intermediate or strong. On a lattice the mapping is restricted to large U, and is controlled by the small parameter 1/ρU. Explicit expressions are given for the low-energy scale, differential conductance, and occupancy of the level in the limit where U is large.

cond-mat.str-el↗
arXiv2007

Nonequilibrium quantum-impurities: from entropy production to information theory

Nonequilibrium steady-state currents, unlike their equilibrium counterparts, continuously dissipate energy into their physical surroundings leading to entropy production and time-reversal symmetry breaking. This letter discusses these issues in the context of quantum impurity models driven out of equilibrium by attaching the impurity to leads at different chemical potentials and temperatures. We start by pointing out that entropy production is often hidden in traditional treatments of quantum-impurity models. We then use simple thermodynamic arguments to define the rate of entropy production. Using the scattering framework recently developed by the authors we show that the rate of entropy production has a simple information theoretic interpretation in terms of the Shannon entropy and Kullback-Leibler divergence of nonequilibrium distribution function. This allows us to show that the entropy production is strictly positive for any nonequilibrium steady-state. We conclude by applying these ideas to the Resonance Level Model and the Kondo model.

cond-mat.str-el↗
arXiv2007

Universal aspects of non-equilibrium currents in a quantum dot

We study the electric current in the non-equilibrium Kondo model at zero magnetic field, using real-time perturbation theory in the Schwinger-Keldysh formulation. We show that the perturbative coefficients to all orders have a finite limit at large switch-on time (t_0 to minus infinity), and we give a prescription for general operators to give finite coefficients in this limit. We explain how this is related to the fact that the leads play the role of thermal baths and allow relaxation to occur and the steady state to form. This proves perturbatively that a steady state is reached in the Schwinger-Keldysh formulation, and specifies which operators correspond to quantities that have a well-defined value in the steady state. Then, we show that the steady state can be described by a special type of density matrix (related to Hershfield's conjecture for the particular example of the non-equilibrium Kondo model.) In the second part of the paper we perform a renormalization-group analysis of the perturbative series. We give a general argument that strongly suggests that the perturbative series of any average in the steady state satisfies the equilibrium Callan-Symanzik equations, and show in detail how it works to one-loop order for the electric current operator inside any average. We finally compute to two loops order the average of the electric current in the steady state, and perform a renormalization-group improvement. From this, we give a universal prescription, valid in the perturbative regime, for comparing the effect of the electric current to that of the temperature on the ``Kondo cloud''.

cond-mat.str-el↗
arXiv2007

Scattering approach to impurity thermodynamics

Recently the authors developed a scattering approach that allows for a complete description of the steady-state physics of quantum-impurities in and out of equilibrium. Quantum impurities are described using scattering eigenstates defined ab initio on the open, infinite line with asymptotic boundary conditions imposed by the leads. The scattering states on the open line are constructed for integrable quantum-impurity models by means of a significant generalization of the Bethe-Ansatz which we call the Scattering Bethe-Ansatz (SBA). The purpose of the paper is to present in detail the scattering approach to quantum-impurity models and the SBA and show that they reproduce well-known thermodynamic results for several widely studied models: the Resonance Level model, Interacting Resonance Level model and the Kondo model. Though the SBA is more complex than the traditional Thermodynamic Bethe Ansatz (TBA) when applied to thermodynamical questions, the scattering approach (SBA) allows access to an array of new questions that cannot be addressed otherwise, ranging from scattering of electrons off magnetic impurities to nonequilibrium dynamics.

cond-mat.str-el↗
arXiv2005

Nonequilibrium Transport in Quantum Impurity Models (Bethe-Ansatz for open systems)

We develop an exact non-perturbative framework to compute steady-state properties of quantum-impurities subject to a finite bias. We show that the steady-state physics of these systems is captured by nonequilibrium scattering eigenstates which satisfy an appropriate Lippman-Schwinger equation. Introducing a generalization of the equilibrium Bethe-Ansatz - the Nonequilibrium Bethe-Ansatz (NEBA), we explicitly construct the scattering eigenstates for the Interacting Resonance Level model and derive exact, nonperturbative results for the steady-state properties of the system.

cond-mat.str-el↗
arXiv2005

Thermal Conductivity of Spin-1/2 Chains

We study the low-temperature transport properties of clean one-dimensional spin-1/2 chains coupled to phonons. Due to the presence of approximate conservation laws, the heat current decays very slowly giving rise to an exponentially large heat conductivity, $κ~ e^{T^*/T}$. As a result of an interplay of Umklapp scattering and spinon-phonon coupling, the characteristic energy scale $T^*$ turns out to be of order $Θ_D/2$, where $Θ_D$ is the Debye energy, rather than the magnetic exchange interaction $J$ -- in agreement with recent measurements in SrCuO compounds. A large magnetic field strongly affects the heat transport by two distinct mechanisms. First, it induces a LINEAR spinon--phonon coupling, which alters the nature of the $T -> 0$ fixed point: the elementary excitations of the system are COMPOSITE SPINON-PHONON objects. Second, the change of the magnetization and the corresponding change of the wave vector of the spinons strongly affects the way in which various Umklapp processes can relax the heat current, leading to a characteristic fractal--like spiky behavior of $κ$ when plotted as a function of magnetization at fixed T.

cond-mat.str-el↗
arXiv2004

Regular and Singular Fermi Liquid fixed points in quantum impurity models

We show that thermodynamics is insufficient to probe the nature of the low energy dynamics of quantum impurity models and a more subtle analysis based on scattering theory is required. Traditionally, quantum impurity models are classified into one of two categories: Fermi liquids and non-Fermi liquids, depending on the analytic properties of the various thermodynamic quntities. We show, however, that even when a quantum impurity model is a Fermi liquid (an incoming electron at the Fermi level scatters elastically off the impurity), one may find singular thermodynamic behavior if characteristics of quasiparticles are not analytic near the Fermi surface. Prompted by this observation, we divide Fermi liquids into two categories: regular Fermi liquids and singular Fermi Liquids. The difference between regular Fermi liquids, singular Fermi liquids, and non-Fermi liquids fixed points is explained using properties of the many-body S-matrix for impurity quasiparticle scattering. Using the Bethe-Ansatz and numerical RG, we show that whereas the ordinary Kondo Model is a regular Fermi liquid the underscreened Kondo model is a a singular Fermi liquid. This results in a breakdown of Nozieres' Fermi liquid picture for the underscreened and explains the singular thermodynamic behavior noticed in Bethe Ansatz and large-N calculations. Furthermore, we show that conventional regular Fermi liquid behavior is re-established in an external magnetic field H, but with a density of states which diverges as 1/H. Possible connections with the field-tuned quantum criticality recently observed in heavy electron materials are also discussed.

cond-mat.str-el↗
arXiv2004

Theory of inelastic scattering from magnetic impurities

We use the numerical renormalization group method tocalculate the single particle matrix elements $\cal T$ of the many body $T$-matrix of the conduction electrons scattered by a magnetic impurity at T=0 temperature. Since $\cal T$ determines both the total and the elastic, spin-diagonal scattering cross sections, we are able to compute the full energy-, spin- and magnetic field dependence of the inelastic scattering cross section, $σ_{\rm inel}(ω)$. We find an almost linear frequency dependence of $σ_{\rm inel}(ω)$ below the Kondo temperature, $T_K$, which crosses over to a $\sim ω^2$ behavior only at extremely low energies. Our method can be generalized to other quantum impurity models.

cond-mat.mes-hall↗
arXiv2003

Low Temperature Transport Properties of Strongly Interacting Systems- Thermal Conductivity of Spin-1/2 Chains

We outline a general approach to the computation of transport properties of interacting systems at low temperetures and frequencies. We show that if the fixed point and the irrelevant operators around it are known, then by studying the structure of the softly violated conserved currents chracterizing the fixed point one may set up an effective calculation in terms of a memory matrix formalism. We apply this approach to the computation of thermal conductivity of spin chains embedded in a matter matrix and interacting with its phonons. The results are found to be in very good agreement with experiment.

cond-mat.str-el↗
arXiv1998

Chiral Liquids in 1-d: A New Class of NFL-Fixed Points

We identify a non Fermi Liquid (NFL) class of fixed points describing the infrared behaviour of interacting chiral fermions in one dimension. The thermodynamic properties and asymptotic correlation functions are characterized by universal exponents, which we determine by means of conformal and Bethe-Ansatz techniques. The mechanism leading to the breakdown of Fermi-Liquid theory is quite general and can be expected to be realized in systems with broken T-invariance. As an example we study the edge states of interacting QHE systems. We calculate the universal frequency dependence of the spin conductance in these systems as well as the NMR response.

cond-mat.str-el↗
arXiv1998

Solution of the Multichannel Coqblin-Schrieffer Impurity Model and Application to Multi-Level systems

A complete Bethe Ansatz solution of the SU(N)xSU(f) Coqblin Schrieffer model and a detailed analysis of some physical applications of the model are given. As in the usual multichannel Kondo model a variety of Fermi liquid and non-Fermi liquid (NFL) fixed points is found, whose nature depends on the impurity representation, $μ$. For $μ=f$ we find a Fermi liquid fixed point, with the impurity spin completely screened. For $f>μ$ the impurity is overscreened and the model has NFL properties. The form the NFL behavior takes depends on the N and f: for $N\le f$ the specific heat and the susceptibility are dominated by the NFL contributions, for N>f the leading contributions are Fermi-liquid like and the NFL behavior can be seen only to subleading order, while for N=f the behavior is marginal. We also analyze the possibility of physical realizations. We show by a detailed renormalization group and 1/f analysis that the tunneling N-state problem can be mapped into the SU(N)xSU(f) exchange model, and discuss the subtle differences between the two models. As another physical realization we suggest a double quantum dot structure that can be described by means of an SU(3)xSU(2) model if the parameters of the dots are tuned appropriately.

cond-mat.str-el↗
arXiv1997

A New Quantum Phase Transition in the Coupled Quantum Dots System

We study two quantum dots in the limit of strong dot-lead coupling and weak dot-dot tunneling. The model maps on Ising-coupled Kondo impurities. We argue that a new quantum critical fixed point exists at an intermediate value of the mutual capacitance, supporting non-Fermi liquid behaviour. We construct the total conductance across the double dot structure. It exhibits a strongly peaked behaviour as a function of the mutual capacitance, gate voltage, and temperature.

cond-mat.mes-hall↗
arXiv1995

Chiral Non-Fermi Liquids in 1-d

We study models of chiral interacting fermions by means of conformal and Bethe-Ansatz techniques, and determine their thermodynamic properties and asymptotic correlation functions. We identify a class of fixed points characterizing the infrared behavior of the models. They display {\it chirally stabilized} non Fermi-Liquid behavior characterized by universal exponents. A realization of these fluids may be found in the edge states of bilayered QHE systems. We calculate the universal temperature dependence of the staggered conductance in these systems.

cond-mat↗