Papers by Alberto Anfossi
Physical Review B Condensed Matter and Materials Physics, 2007
The role of two-point and multipartite entanglement at quantum phase transitions (QPTs) in correl... more 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.
Physical Review B Condensed Matter and Materials Physics, Feb 1, 2006
We investigate the transition to the insulating state in the one-dimensional Hubbard model with b... more 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 uc(x) for x≳0.5 . The region 0<u<uc turns out to have a superconducting nature, at least for not too large x>xc .
... The elementary excitations of the exactly solvable Russian doll BCS model of superconductivit... more ... The elementary excitations of the exactly solvable Russian doll BCS model of superconductivity. ... The model was first studied using RG, mean field and numerical methods showing the Russiandoll scaling of the spectrum, E n ~ E 0 e - λn , where λ is the RG period. ...
Physical Review Letters, 2005
We analyze correlations between subsystems for an extended Hubbard model exactly solvable in one ... more 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. PACS numbers: 03.67.Ud, In the past years, the characterization of complex quantum phenomena has received a strong impulse from the recent developments in quantum-information theory. Within such framework, a crucial notion is that of entanglement. Besides being recognized as a fundamental resource for quantum computation and communication tasks , it has also been used to better characterize the critical behavior of different manybody quantum systems when some characteristic parameter of the related Hamiltonian is varied; the latter phenomenon being known as quantum phase transition (QPT) . In fact, a deep comprehension of universal properties of QPTs has not been fully reached yet. The peculiarity of using entanglement in this context is that, being a single direct measure of quantum correlations, it should allow for a unified treatment of QPTs; at least, whenever the occurring QPT is to ascribe to the quantum nature of the system, which is always the case at T = 0 since thermal fluctuations are absent. A first description of the relations between entanglement of one or two spins and QPTs in spin-1/2 chains was given in , where it was noticed how derivatives of concurrence show divergencies in correspondence of QPT, with appropriate scaling exponents. The entanglement of blocks of L spins and its scaling behavior in spin models showing critical behavior was then investigated in . The problem of characterizing the ground state phase diagram of fermionic systems by means of entanglement has been addressed more recently in , where it was shown how the study of single-site entanglement allows one to reproduce the relevant features of the known (numerical) phase diagram. While this is a promising starting point, it remains to be clarified which quantum correlations are responsible for the occurring QPT: if two-points or shared (multipartite), if short or long ranged. The answer to the above issue would in fact require exhaustive investigation of the entanglement between any two subsystems. In case the subsystems have just two degrees of freedom, concurrence properly quantifies the quantum correlations . A generalization of such quantity to (sub)systems with a higher number of degrees of freedom D has been proposed, and is known as negativity . Also, the total amount of correlations between any two subsystems is captured by quantum mutual information .
Physical Review Letters, 2007
We determine the quantum phase diagram of the one-dimensional Hubbard model with bondcharge inter... more We determine the quantum phase diagram of the one-dimensional Hubbard model with bondcharge interaction X in addition to the usual Coulomb repulsion U > 0 at half-filling. For large enough X < t the model shows three phases. For large U the system is in the spin-density wave phase as in the usual Hubbard model. As U decreases, there is first a spin transition to a spontaneously dimerized bond-ordered wave phase and then a charge transition to a novel phase in which the dominant correlations at large distances correspond to an incommensurate singlet superconductor.
Physical Review B, 2008
We investigate entanglement properties at quantum phase transitions of an integrable extended Hub... more 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 η-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.
Physical Review A, 2009
We show that the Hubbard Hamiltonian with particle-assisted tunneling rates -recently proposed to... more 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 pc.
Physical Review A, 2010
Strongly interacting fermionic atoms on optical lattices are studied through a Hubbard-like model... more 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 on-site 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 = 4g 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 in the number of doubly occupied sites under the intermediate coupling regime, thus providing a criterion for extracting from measurements the effective value of g.
Journal of Physics A: Mathematical and General, 2005
We revisit the Jordan-Wigner transformation, showing that -rather than a non-local isomorphism be... more 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. PACS numbers: 2003 PACS number(s): 75.10.Jm,05.30.-d,03.65.Fd,71.10.-w
Arxiv preprint cond-mat/0412532, 2004
We review the approach of generalized permutator to produce a class of integrable quantum Hamilto... more 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. 2003 PACS number(s): 71.10.Pm; 71.27.+a; 05.30.-d;02.30.Ik
Physical Review B, 2009
We investigate numerically at various fillings the ground state of the one-dimensional Hubbard mo... more 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 large range of filling values n around half filling, and for repulsive Coulomb interaction u ≤ uc(x, n), phase separation at a nanoscale (NPS phase) between two conducting phases at different densities occurs when x 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 x 2/3 a crossover to a homogeneous phase, still superconducting, takes place.
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Papers by Alberto Anfossi