arXiv subjects

Arianna Montorsi

Publications and source records attributed to Arianna Montorsi.

At least 37 records · Page 2Linked to original sources

arXiv2011

Quantum discord and classical correlations in the bond-charge Hubbard model: quantum phase transitions, ODLRO and violation of the monogamy property for discord

We study the quantum discord (QD) and the classical correlations (CC) in a reference model for strongly correlated electrons, the one-dimensional bond-charge extended Hubbard model. We show that the comparison of QD and CC and of their derivatives in the direct and reciprocal lattice allows one to efficiently inspect the structure of two-point driven quantum phase transitions (QPTs), discriminating those at which off diagonal long range order (ODLRO) is involved. Moreover we observe that QD between pair of sites is a monotonic function of ODLRO, thus establishing a direct relation between the latter and two point quantum correlations different from the entanglement. The study of the ground state properties allows to show that for a whole class of permutation invariant (η-pair) states quantum discord can violate the monogamy property, both in presence and in absence of bipartite entanglement. In the thermodynamic limit, due to the presence of ODLRO, the violation for η-pair states is maximal, while for the purely fermionic ground state is finite. From a general perspective, all our results validate the importance of the concepts of QD and CC for the study of critical condensed-matter systems.

quant-ph↗

arXiv2010

Hidden XY structure of the bond-charge Hubbard model

The repulsive one-dimensional Hubbard model with bond-charge interaction (HBC) in the superconducting regime is mapped onto the spin-1/2 XY model with transverse field. We calculate correlations and phase boundaries, realizing an excellent agreement with numerical results. The critical line for the superconducting transition is shown to coincide with the analytical factorization line identifying the commensurate-incommensurate transition in the XY model.

cond-mat.str-el↗

arXiv2010

Detecting the tunneling rates for strongly interacting fermions on optical lattices

Strongly interacting fermionic atoms on optical lattices are studied through a Hubbard-like model Hamiltonian, in which tunneling rates of atoms and molecules between neighboring sites are assumed to be different. In the limit of large onsite repulsion U, the model is shown to reproduce the t-J Hamiltonian, in which the J coefficient of the Heisenberg term depends on the particle-assisted tunneling rate g: explicitly, $J=4 g^2/U$. At half-filling, g drives a crossover from a Brinkman-Rice paramagnetic insulator of fully localized atoms (g=0) to the antiferromagnetic Mott insulator of the standard Hubbard case (g=t). This is observed already at the intermediate coupling regime in the number of doubly occupied sites, thus providing a criterion to extract from measurements the effective value of g.

cond-mat.other↗

arXiv2009

Phase diagram of imbalanced strongly interacting fermions on a one-dimensional optical lattice

We show that the Hubbard Hamiltonian with particle-assisted tunneling rates --recently proposed to model a fermionic mixture near a broad Feshbach resonance-- displays a ground state phase diagram with superfluid, insulating, and phase separated regimes. In the latter case, when the populations are balanced the two phases coexist in microscopic antiferromagnetic domains. Macroscopic phase segregation into a high-density superfluid of molecules, and a low-density Fermi liquid of single atoms appears in the density profile above a critical polarization p_c.

quant-ph↗

arXiv2009

Nanoscale phase separation and superconductivity in the one-dimensional Hirsch model

We investigate numerically at various fillings the ground state of the one-dimensional Hubbard model with correlated hopping x (Hirsch model). It is found that, for a wide range of filling values n around half filling, and for repulsive Coulomb interaction u\leq u_c(x,n), phase separation at a nanoscale (NPS phase) between two conducting phases at different densities occurs when x\gtrsim 2/3. The NPS phase is accompanied by the opening of a spin gap and the system behaves as a Luther-Emery Liquid with dominant superconducting correlations. Close to half filling, an anomalous peak emerges in the charge structure factor related to the density of doubly occupied sites, which determines the size of the droplets in the NPS phase. For 1/2\lesssim x\lesssim 2/3 a crossover to a homogeneous phase, still superconducting, takes place.

cond-mat.str-el↗

arXiv2008

Phase separation in fermionic systems with particle-hole asymmetry

We determine the ground-state phase-diagram of a Hubbard Hamiltonian with correlated hopping, which is asymmetric under particle-hole transform. By lowering the repulsive Coulomb interaction U at appropriate filling and interaction parameters, the ground state separates into a hole and an electron conducting phases: two different wave vectors characterize the system and charge-charge correlations become incommensurate. By further decreasing U another transition occurs at which the hole conducting region becomes insulating, and conventional phase separation takes place. Finally, for negative U the whole system eventually becomes a paired insulator. It is speculated that such behavior could be at the origin of the incommensurate superconducting phase recently discovered in the 1D Hirsch model. The exact phase boundaries are calculated in one dimension.

cond-mat.str-el↗

arXiv2008

Momentum-space analysis of multipartite entanglement at quantum phase transitions

We investigate entanglement properties at quantum phase transitions of an integrable extended Hubbard model in the momentum space representation. Two elementary subsystems are recognized: the single mode of an electron, and the pair of modes (electrons coupled through the eta-pairing mechanism). We first detect the two/multi-partite nature of each quantum phase transition by a comparative study of the singularities of Von Neumann entropy and quantum mutual information. We establish the existing relations between the correlations in the momentum representation and those exhibited in the complementary picture: the direct lattice representation. The presence of multipartite entanglement is then investigated in detail through the Q-measure, namely a generalization of the Meyer-Wallach measure of entanglement. Such a measure becomes increasingly sensitive to correlations of a multipartite nature increasing the size of the reduced density matrix. In momentum space, we succeed in obtaining the latter for our system at arbitrary size and we relate its behaviour to the nature of the various QPTs.

quant-ph↗

arXiv2007

Entanglement in extended Hubbard models and quantum phase transitions

The role of two-point and multipartite entanglement at quantum phase transitions (QPTs) in correlated electron systems is investigated. We consider a bond-charge extended Hubbard model exactly solvable in one dimension which displays various QPTs, with two (qubit) as well as more (qudit) on-site degrees of freedom involved. The analysis is carried out by means of appropriate measures of bipartite/multipartite quantum correlations. It is found that all transitions ascribed to two-point correlations are characterized by an entanglement range which diverges at the transition points. The exponent coincides with that of the correlation length at the transitions. We introduce the correlation ratio, namely, the ratio of quantum mutual information and single-site entanglement. We show that at T=0, it captures the relative role of two-point and multipartite quantum correlations at transition points, generalizing to qudit systems the entanglement ratio. Moreover, a finite value of quantum mutual information between infinitely distant sites is seen to quantify the presence of off-diagonal long-range order induced by multipartite entanglement.

cond-mat.str-el↗

arXiv2007

Single-site entanglement at superconductor-insulator transition in the Hirsch model

We investigate the transition to the insulating state in the one-dimensional Hubbard model with bond-charge interaction x (Hirsch model), at half-filling and T=0. By means of the density-matrix renormalization group algorithm the charge gap closure is examined by both standard finite size scaling analysis and looking at singularities in the derivatives of single-site entanglement. The results of the two techniques show that a quantum phase transition takes place at a finite Coulomb interaction u_c(x) for x>0.5. The region 0 x_c.

cond-mat.str-el↗

arXiv2005

Recent results on integrable electronic models

We review the approach of generalized permutator to produce a class of integrable quantum Hamiltonians, as well as the technique of Sutherland species (SS) to map a subclass of it into solvable spinless fermions models. In particular, we apply the above scheme to construct integrable interacting electron Hamiltonians: first we review the extended Hubbard case, discussing both ground state and thermodynamics; then we pass to constrained fermion models, generating 56 integrable cases, among which both supersymmetric t-J model and infinite U Hubbard model are obtained, as well as other physically interesting cases, such as a particular t-V model. For the latter we describe how the complete spectrum can be gained by means of SS technique. Finally we speculate about possible applications to spin S models.

cond-mat.str-el↗

arXiv2005

Two-Point Versus Multipartite Entanglement in Quantum Phase Transitions

We analyze correlations between subsystems for an extended Hubbard model exactly solvable in one dimension, which exhibits a rich structure of quantum phase transitions (QPTs). The T=0 phase diagram is exactly reproduced by studying singularities of single-site entanglement. It is shown how comparison of the latter quantity and quantum mutual information allows one to recognize whether two-point or shared quantum correlations are responsible for each of the occurring QPTs. The method works in principle for any number D of degrees of freedom per site. As a by-product, we are providing a benchmark for direct measures of bipartite entanglement; in particular, here we discuss the role of negativity at the transition.

cond-mat.str-el↗

arXiv2005

Spin-fermion mappings for even Hamiltonian operators

We revisit the Jordan-Wigner transformation, showing that --rather than a non-local isomorphism between different fermionic and spin Hamiltonian operators-- it can be viewed in terms of local identities relating different realizations of projection operators. The construction works for arbitrary dimension of the ambient lattice, as well as of the on-site vector space, generalizing Jordan-Wigner's result. It provides direct mapping of local quantum spin problems into local fermionic problems (and viceversa), under the (rather physical) requirement that the latter are described by Hamiltonian's which are even products of fermionic operators. As an application, we specialize to mappings between constrained-fermions models and spin 1 models on chains, obtaining in particular some new integrable spin Hamiltonian, and the corresponding ground state energies.

cond-mat.str-el↗

arXiv2002

Finite-temperature properties of the Hubbard chain with bond-charge interaction

We investigate the one-dimensional Hubbard model with an additional bond-charge interaction, recently considered in the description of compounds that exhibit strong 1D features above the temperature of ordered phases. The partition function of the model is exactly calculated for a value of the bond-charge coupling; the behavior of the specific heat and spin susceptibility as a function of temperature is derived at arbitrary filling, and particularly discussed across the occurring metal-insulator transition. The results show that the bond-charge terms weaken the spin excitations of the system.

cond-mat.str-el↗

arXiv1999

Integrable Extended Hubbard Hamiltonians from Symmetric Group Solutions

We consider the most general form of extended Hubbard Hamiltonian conserving the total spin and number of electrons, and find all the 1-dimensional completely integrable models which can be derived from first degree polynomial solution of the Yang-Baxter equation. It is shown that such models are 96. They are identified with the 16-dimensional representation of a new class of solutions of symmetric group relations, acting as generalized permutators. As particular examples, the EKS and some other known models are obtained.

cond-mat.str-el↗

arXiv1999

Temperature and filling dependence of the superconducting $π$-phase in the Penson-Kolb-Hubbard model

We investigate in the Hartree Fock approximation the temperature and filling dependence of the superconducting $π$-phase for the Penson-Kolb-Hubbard model. Due to the presence of the pair-hopping term, the phase survives for repulsive values of the on-site Coulomb interaction, exhibiting an interesting filling and temperature dependence. The structure of the self-consistent equations peculiar to the $π$-phase of the model allows to explicitly solve them for the chemical potential. The phase diagrams are shown and discussed in dimension 2 and 3. We also show that, when a next-nearest neighbours hopping term is included, the critical temperature of the superconducting region increases, and the corresponding range of filling values is shifted away from half-filling. Comparison with known exact results is also discussed.

cond-mat.str-el↗

arXiv1999

Spin picture of the one-dimensional Hubbard model: Two-fluid structure and phase dynamics

We propose a scheme for investigating the quantum dynamics of interacting electron models by means of time-dependent variational principle and spin coherent states of space lattice operators. We apply such a scheme to the one-dimensional hubbard model, and solve the resulting equations in different regimes. In particular, we find that at low densities the dynamics is mapped into two coupled nonlinear Schroedinger equations, whereas near half-filling the model is described by two coupled Josephson junction arrays. Focusing then to the case in which only the phases of the spin variables are dynamically active, we examine a number of different solutions corresponding to the excitations of few macroscopic modes. Based on fixed point equation of the simpler among them, we show that the standard one-band ground state phase space is found.

cond-mat.supr-con↗

arXiv1996

Dynamics of the Hubbard model: a general approach by time dependent variational principle

We describe the quantum dynamics of the Hubbard model at semi-classical level, by implementing the Time-Dependent Variational Principle (TDVP) procedure on appropriate macroscopic wavefunctions constructed in terms of su(2)-coherent states. Within the TDVP procedure, such states turn out to include a time-dependent quantum phase, part of which can be recognized as Berry's phase. We derive two new semi-classical model Hamiltonians for describing the dynamics in the paramagnetic, superconducting, antiferromagnetic and charge density wave phases and solve the corresponding canonical equations of motion in various cases. Noticeably, a vortex-like ground state phase dynamics is found to take place for U>0 away from half filling. Moreover, it appears that an oscillatory-like ground state dynamics survives at the Fermi surface at half-filling for any U. The low-energy dynamics is also exactly solved by separating fast and slow variables. The role of the time-dependent phase is shown to be particularly interesting in the ordered phases.

cond-mat.str-el↗

arXiv1995

Rigorous results on superconducting ground states for attractive extended Hubbard models

We show that the exact ground state for a class of extended Hubbard models including bond-charge, exchange, and pair-hopping terms, is the Yang "eta-paired" state for any non-vanishing value of the pair-hopping amplitude, at least when the on-site Coulomb interaction is attractive enough and the remaining physical parameters satisfy a single constraint. The ground state is thus rigorously superconducting. Our result holds on a bipartite lattice in any dimension, at any band filling, and for arbitrary electron hopping.

cond-mat↗