Papers by Artemio Gonzalez-Lopez
We introduce a new class of generalized Lipkin-Meshkov-Glick models with su(m + 1) spin and long-... more We introduce a new class of generalized Lipkin-Meshkov-Glick models with su(m + 1) spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of su(m + 1) type. We evaluate in closed form the reduced density matrix of a block of L spins when the whole system is in its ground state, and study the corresponding von Neumann and Rényi entanglement entropies in the thermodynamic limit. We show that both of these entropies scale as a log L when L tends to infinity, and that the coefficient a is equal to (m − k)/2 in the ground state phase with k vanishing su(m + 1) magnon densities. Our results suggest that the class of generalized Lipkin-Meshkov-Glick models contains a critical model in each of the m + 1 ground-state phases, effectively described by a conformal field theory with m − k bosons and m − k fermions. We have also computed the Tsallis entanglement entropy of the ground state of these generalized su(m + 1) Lipkin-Meshkov-Glick models, finding that it can be made extensive by an appropriate choice of its parameter only when m − k 3. Finally, in the su(3) case we construct in detail the phase diagram of the ground state in parameter space, showing that it is determined in a simple way by the fundamental su(3) weights. This is also true in the su(m + 1) case; for instance, we prove that the region for which all the magnon densities are non-vanishing is an (m + 1)-simplex in R m whose vertices are the fundamental su(m + 1) weights.
Annals of Physics, 2018
We completely solve the problem of classifying all one-dimensional quantum potentials with neares... more We completely solve the problem of classifying all one-dimensional quantum potentials with nearest-and next-to-nearest-neighbors interactions whose ground state is Jastrowlike, i.e., of Jastrow type but depending only on differences of consecutive particles. In particular, we show that these models must necessarily contain a three-body interaction term, as was the case with all previously known examples. We discuss several particular instances of the general solution, including a new hyperbolic potential and a model with elliptic interactions which reduces to the known rational and trigonometric ones in appropriate limits.
Journal of Statistical Mechanics: Theory and Experiment, 2017
We introduce a class of generalized Lipkin-Meshkov-Glick (gLMG) models with su(m) interactions of... more We introduce a class of generalized Lipkin-Meshkov-Glick (gLMG) models with su(m) interactions of Haldane-Shastry type. We have computed the partition function of these models in closed form by exactly evaluating the partition function of the restriction of a spin chain Hamiltonian of Haldane-Shastry type to subspaces with well-defined magnon numbers. As a byproduct of our analysis, we have obtained strong numerical evidence of the Gaussian character of the level density of the latter restricted Hamiltonians, and studied the distribution of the spacings of consecutive unfolded levels. We have also discussed the thermodynamic behavior of a large family of su(2) and su(3) gLMG models, showing that it is qualitatively similar to that of a two-level system.
Physical Review B, 2016
In this paper we study an su(m)-invariant open version of the Haldane-Shastry spin chain whose gr... more In this paper we study an su(m)-invariant open version of the Haldane-Shastry spin chain whose ground state can be obtained from the chiral correlator of the c = m − 1 free boson boundary conformal field theory. We show that this model is integrable for a suitable choice of the chain sites depending on the roots of the Jacobi polynomial P β−1,β ′ −1 N , where N is the number of sites and β, β ′ are two positive parameters. We also compute in closed form the first few nontrivial conserved charges arising from the twisted Yangian invariance of the model. We evaluate the chain's partition function, determine the ground state energy and deduce a complete description of the spectrum in terms of Haldane's motifs and a related classical vertex model. In particular, this description entails that the chain's level density is normally distributed in the thermodynamic limit. We also analyze the spectrum's degeneracy, proving that it is much higher than for a typical Yangian-invariant model.
Scientific Reports, 2017
The analysis of the entanglement entropy of a subsystem of a one-dimensional quantum system is a ... more The analysis of the entanglement entropy of a subsystem of a one-dimensional quantum system is a powerful tool for unravelling its critical nature. For instance, the scaling behaviour of the entanglement entropy determines the central charge of the associated Virasoro algebra. For a free fermion system, the entanglement entropy depends essentially on two sets, namely the set A of sites of the subsystem considered and the set K of excited momentum modes. In this work we make use of a general duality principle establishing the invariance of the entanglement entropy under exchange of the sets A and K to tackle complex problems by studying their dual counterparts. The duality principle is also a key ingredient in the formulation of a novel conjecture for the asymptotic behavior of the entanglement entropy of a free fermion system in the general case in which both sets A and K consist of an arbitrary number of blocks. We have verified that this conjecture reproduces the numerical results with excellent precision for all the configurations analyzed. We have also applied the conjecture to deduce several asymptotic formulas for the mutual and r-partite information generalizing the known ones for the single block case.
Physical review. E, 2017
We study the critical behavior and the ground-state entanglement of a large class of su(1|1) supe... more We study the critical behavior and the ground-state entanglement of a large class of su(1|1) supersymmetric spin chains with a general (not necessarily monotonic) dispersion relation. We show that this class includes several relevant models, with both short- and long-range interactions of a simple form. We determine the low temperature behavior of the free energy per spin, and deduce that the models considered have a critical phase in the same universality class as a (1+1)-dimensional conformal field theory (CFT) with central charge equal to the number of connected components of the Fermi sea. We also study the Rényi entanglement entropy of the ground state, deriving its asymptotic behavior as the block size tends to infinity. In particular, we show that this entropy exhibits the logarithmic growth characteristic of (1+1)-dimensional CFTs and one-dimensional (fermionic) critical lattice models, with a central charge consistent with the low-temperature behavior of the free energy. Ou...
Physical Review E, 2016
We introduce a general class of su(1|1) supersymmetric spin chains with long-range interactions w... more We introduce a general class of su(1|1) supersymmetric spin chains with long-range interactions which includes as particular cases the su(1|1) Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the su(1|1) permutation operator, and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low energy excitations and the low temperature behavior of the free energy, which coincides with that of a (1 + 1)-dimensional conformal field theory (CFT) with central charge c = 1 when the chemical potential lies in the critical interval (0, E(π)), E(p) being the dispersion relation. We also analyze the von Neumann and Rényi ground state entanglement entropies, showing that they exhibit the logarithmic scaling with the size of the block of spins characteristic of a one-boson (1 + 1)-dimensional CFT. Our results thus show that the models under study are quantum critical when the chemical potential belongs to the critical interval, with central charge c = 1. From the analysis of the fermion density at zero temperature, we also conclude that there is a quantum phase transition at both ends of the critical interval. This is further confirmed by the behavior of the fermion density at finite temperature, which is studied analytically (at low temperature), as well as numerically for the su(1|1) elliptic chain.
Physics Letters A, 1988
In this paper, the connection between point symmetries and the integrability by quadratures of se... more In this paper, the connection between point symmetries and the integrability by quadratures of second-order ordinary differential equations is discussed. An example is given of a family of second-order ordinary differential equations integrable by quadratures whose point symmetry group is, nevertheless, trivial. This refutes the widespread belief that the existence of nontrivial point symmetries is a necessary condition for the integrability by quadratures ofordinary differential equations. The significance ofdynamical (versus point) symmetries in this field is illustrated with a few recent results.
Journal of Physics A: Mathematical and General, 1994
Sharp upper bounds on the dimension of the Lie algebra of inhibsimal variational and divergence p... more Sharp upper bounds on the dimension of the Lie algebra of inhibsimal variational and divergence point symmehies of a non-uivial Lagrangian L(x. U, U', . . . , U("))@, U E Ut) of arbitmy order n are found. For any given order, all Lagrangians whose Lie algebra of variational or of divergence symmeuies is of maximal dimension are completely classified, modulo l o a l point transformations. It is shown, in particular. that for n 2 2 the algebra of variational symmeuies of the generalized h e particle Lagrangian (U("))* is not of maximal dimension, whereas when n = 1 there are several Lagrangians admithg a variational s y m e h y algebra of maximal dimendon and generating differential equations different kom the free particle equation. A connection between variational problems on the line and scalar evolution equations in one time and one space variables is also established, showing that Lagrangians with a variational symmehy algebra of maximal dimension correspond to evolution equations with a " a l Lie algebra of time-preserving time-independent infinitesimal point symmetries. The technique used in the proof of the above results is applied to give a simple proof of the fact that an ordinary differential equation of order n > 2 has a symmetry algebra. of maximal dimension if and only if it is locally equivalent under a point transformation to the generalized free particle equation "(4 = 0.
AIP Conference Proceedings, 2001
New Trends in Integrability and Partial Solvability, 2004
We describe a general method for constructing (scalar or spin) Calogero-Sutherland models of A n ... more We describe a general method for constructing (scalar or spin) Calogero-Sutherland models of A n or BC N type, which are either exactly or quasi-exactly solvable. Our approach is based on the simultaneous use of three different families of Dunkl operators of each type, one of which was recently introduced by the authors. We perform a complete classification of the models which can be constructed by our method. We obtain in this way several new families of (quasi-)exactly solvable Calogero-Sutherland models, some of them with elliptic interactions.
Lettere al Nuovo Cimento, 1984
Symmetry and Perturbation Theory, 2003
We solve in closed form the simplest (su(1|1)) supersymmetric version of Inozemtsev's elliptic sp... more We solve in closed form the simplest (su(1|1)) supersymmetric version of Inozemtsev's elliptic spin chain, as well as its infinite (hyperbolic) counterpart. The solution relies on the equivalence of these models to a system of free spinless fermions, and on the exact computation of the Fourier transform of the resulting elliptic hopping amplitude. We also compute the thermodynamic functions of the finite (elliptic) chain and their low temperature limit, and show that the energy levels become normally distributed in the thermodynamic limit. Our results indicate that at low temperatures the su(1|1) elliptic chain behaves as a critical XX model, and deviates in an essential way from the Haldane-Shastry chain.
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Papers by Artemio Gonzalez-Lopez