arXiv subjects

Jean Richert

Publications and source records attributed to Jean Richert.

32 records · Page 2Linked to original sources

arXiv2006

Strict site-occupation constraint in 2d Heisenberg models and dynamical mass generation in $QED_3$ at finite temperature

We study the effect of site occupation in 2d quantum spin systems at finite temperature in a $π$-flux state description at the mean-field level. We impose each lattice site to be occupied by a single SU(2) spin. This is realized by means of a specific prescription. We consider the low-energy Hamiltonian which is mapped into a $QED_3$ Lagrangian of spinons. We compare the dynamically generated mass to the one obtained by means of an average site occupation constraint.

cond-mat.str-el↗

arXiv2005

Magnetic properties of antiferromagnetic quantum Heisenberg spin systems with a strict single particle site occupation

We work out the magnetization and susceptibility of Heisenberg- and XXZ-model antiferromagnet spin-1/2 systems in $D$ dimensions under a rigorous constraint of single particle site occupancy. Quantum fluctuations are taken into account up to the first order in a loop expansion beyond the Néel state mean field solution. We discuss the results, their validity in the vicinity of the critical point and compare them with the results obtained by means of a spin wave approach.

cond-mat.str-el↗

arXiv2005

A variational approach to the low energy properties of even-legged d-dimensional quantum spin systems

We develop a variational formalism in order to study the structure of low energy spectra of frustrated quantum spin systems. It is first applied to trial wavefunctions of ladders with one spin-1/2 on each site. We determine energy minima of these states. The variational ground state shows a finite energy gap with respect to the energies of states which span the Hilbert space and are orthogonal to it. This is the case for any size of the system. Under some justifiable approximations the argument can be extended to even-legged ladder systems in 2d and higher dimensional spaces. The Hamiltonian can contain spin-spin coupling interactions of any range. For specific values of the coupling strengths level degeneracies can occur.

cond-mat.str-el↗

arXiv2005

Site occupation constraints in mean-field approaches of quantum spin systems at finite temperature

We study the effect of site occupation on the description of quantum spin systems at finite temperature and mean-field level. We impose each lattice site to be occupied by a single electron. This is realized by means of a specific prescription. The outcome of the prescription is compared to the result obtained by means of a projection procedure which fixes the site occupation to one particle per site on an average. The comparison is performed for different representations of the Hamiltonian in Fock space leading to different types of mean-field solutions. The behaviour of order parameters is analyzed for each choice of the mean-field and constraint which fixes the occupation rate at each site. Sizable quantitative differences between the outcomes obtained with the two different constraints are observed.

cond-mat.str-el↗

arXiv2005

Ageing without detailed balance in the bosonic contact and pair-contact processes: exact results

Ageing in systems without detailed balance is studied in the exactly solvable bosonic contact process and the critical bosonic pair-contact process. The two-time correlation function and the two-time response function are explicitly found. In the ageing regime, the dynamical scaling of these is analyzed and exact results for the ageing exponents and the scaling functions are derived. For the critical bosonic pair-contact process the autocorrelation and autoresponse exponents agree but the ageing exponents $a$ and $b$ are shown to be distinct.

cond-mat.stat-mech↗

arXiv2003

Renormalisation and fixed points in Hilbert Space

The energies of low-lying bound states of a microscopic quantum many-body system of particles can be worked out in a reduced Hilbert space. We present here and test a specific non-perturbative truncation procedure. We also show that real exceptional points which may be present in the spectrum can be identified as fixed points of coupling constants in the truncation procedure.

quant-ph↗

arXiv2003

Competition between dynamic and thermal relaxation in non-equilibrium spin systems above the critical point

We study the long-time behaviour and the spatial correlations of a simple ferromagnetic spin system whose kinetics is governed by a thermal bath with a time-dependent temperature which is characterized by a given external relaxation time tau. Exact results are obtained in the framework of the spherical model in d dimensions. In the paramagnetic phase, the long-time kinetics is shown to depend crucially on the ratio between tau and the internal equilibration time tau_eq. If tau is less than tau_eq, the model relaxes rapidly towards an equilibrium state but there appear transient and spatially oscillating contributions in the spin-spin correlation function. On the other hand, if tau is much greater than tau_eq the system is clamped and its time evolution is delayed with respect to the one of the heat bath. For waiting times s such that tau << s << tau_eq, a quasi-stationary state is found where the fluctuation-dissipation theorem does not hold.

cond-mat.stat-mech↗

arXiv2002

Two Interacting Electrons in a Disorder Potential: Localization Properties

Two electrons move in a quasi one--dimensional wire under the influence of a short--range interaction. We restrict Hilbert space to those states where the two electrons are close to each other. Using supersymmetry, we present a complete analytical solution to this problem. The two--body interaction affects the density of states and, thereby, the localization length. We derive a criterion for the onset of changes of the localization length due to the two--body interaction.

cond-mat.dis-nn↗

arXiv2002

Localization Properties of Two Interacting Electrons in a Disordered Quasi One-Dimensional Potential

We study the transport properties of two electrons in a quasi one-dimensional disordered wire. The electrons are subject to both, a disorder potential and a short range two-body interaction. Using the approach developed by Iida et al. [ Ann. Phys. (N.Y.) 200 (1990) 219 ], the supersymmetry technique, and a suitable truncation of Hilbert space, we work out the two-point correlation function in the framework of a non-linear sigma model. We study the loop corrections to arbitrary order. We obtain a remarkably simple and physically transparent expression for the change of the localization length caused by the two-body interaction.

cond-mat.dis-nn↗

arXiv2001

Functional Callan-Symanzik Equation for the Coulomb Gas

A non-perturbative scheme, based on the functional generalization of the Callan-Symanzik equation is developed to treat the Coulomb interaction in an electron gas. The one-particle irreducible vertex functions are shown to satisfy an evolution equation whose initial condition is given by means of the classical action and the final point corresponds to the physical system. This equation is truncated by expanding it in momenta and excitation energies, leaving the electric charge as an arbitrary, not necesseraly small parameter. Exact coupled partial differential equations up to first order in the frequencies and excitation energies are derived. The numerical integration of these eqations is left to a later stage. Nevertheless, in order to demonstrate the relation with the perturbation expansion the one-loop Lindhard function and screening are reproduced in the independent mode approximation of the evolution equation.

cond-mat.str-el↗

arXiv2000

Modelling static impurities

A simple model is presented for the calculation of the quenched average over impurities which are rendered static by setting their mass equal to infinity. The path integral formalism of the second quantized theory contains annealed averages only. The similarity with the Gaussian quenched potential model is discussed.

cond-mat.dis-nn↗

arXiv2000

An effective theory for conductance by symmetry breaking

An effective theory is suggested for the particle-anti particle and the particle-particle modes of strongly disordered electron systems. The effective theory is studied in the framework of the saddle point expansion and found to support a vacuum which is not invariant under translations in imaginary time. The Goldstone bosons of this symmetry breaking generate a pole in the density-density correlation function. The condensate of the auxiliary field corresponding to the particle-particle channel produces conductivity without relying on the long range fluctuations. The results are obtained for $d>1$.

cond-mat.str-el↗

arXiv2000

Does localization occur in a hierarchical random-matrix model for many-body states?

We use random-matrix theory and supersymmetry techniques to work out the two-point correlation function between states in a hierarchical model which employs Feshbach's chaining hypothesis: Classes of many-body states are introduced. Only states within the same or neighboring classes are coupled. We assume that the density of states per class grows monotonically with class index. The problem is mapped onto a one-dimensional non-linear sigma model. In the limit of a large number of states in each class we derive the critical exponent for the growth of the level density with class index for which delocalization sets in. From a realistic modelling of the class-dependence of the level density, we conclude that the model does not predict Fock-space localization in nuclei.

nucl-th↗

arXiv1998

Properties of low-lying states in a diffusive quantum dot and Fock-space localization

Motivated by an experiment by Sivan et al. (Europhys. Lett. 25, 605 (1994)) and by subsequent theoretical work on localization in Fock space, we study numerically a hierarchical model for a finite many-body system of Fermions moving in a disordered potential and coupled by a two-body interaction. We focus attention on the low-lying states close to the Fermi energy. Both the spreading width and the participation number depend smoothly on excitation energy. This behavior is in keeping with naive expectations and does not display Anderson localization. We show that the model reproduces essential features of the experiment by Sivan et al.

cond-mat.mes-hall↗