arXiv subjects
Publications and source records attributed to G. A. P. Ribeiro.
We study the influence of boundary conditions on the entropy of the six-vertex model. We consider the case of fixed boundary conditions in order to argue that the entropy of the six-vertex model vary continuously from its value for ferroelectric to periodic boundary conditions. This is done by merging the ferroelectric boundary and the Néel boundary.
We study the dependence of entropy [per lattice site] of six-vertex model on boundary conditions. We start with lattices of finite size and then proceed to thermodynamic limit. We argue that the six-vertex model with periodic, anti-periodic and mixed boundary conditions produce the same free-energy in the thermodynamic limit. We have found fixed boundary conditions such that the entropy varies continously from zero to its value for periodic boundary condition. We have also shown that the physical quantities of the six-vertex model at the isotropic point does not change in the case of singular toroidal boundary.
We study the thermodynamic limit of the six-vertex model with domain wall boundary and reflecting end. We evaluated the partition function explicitly in special cases. We calculated the homogeneous limit of the Tsuchiya determinant formula for the partition function. We evaluated the thermodynamic limit and obtain the free energy of the six-vertex model with reflecting end. We determined the free energy in the disordered regime.
We study the magnetocaloric effect for the integrable antiferromagnetic Heisenberg spin chain with competing interactions. We computed the Grüneisen parameter, which is closely related to the magnetocaloric effect, for the quantum spin chain in the thermodynamical limit. This is obtained by means of the solution of a set of non-linear integral equations, which describes the thermodynamics of the model. We also provide results for the entropy $S$ and the isentropes in the $(H,T)$ plane.
We consider integrable quantum spin chains with competing interactions. We apply the quantum transfer matrix approach to these spin chains. This allowed us to derive a set of non-linear integral equations for the thermodynamics of these spin chains. We provide numerical solution of these integral equations for the entropy as function of magnetic field, temperature and the coupling constant. This allow us to assess, at low but finite temperature, the picture describing the ground state diagram for high spin chain and longer range interchain interactions.
In this paper we study the spectrum of the spin-1 Temperley-Lieb spin chain with integrable open boundary conditions. We obtain the eigenvalue expressions as well as its associated Bethe ansatz equations by means of the coordinate Bethe ansatz. These equations provide the complete description of the spectrum of the model.
We review the main results and ideas showing that quantum correlations at finite temperatures (T), in particular quantum discord, are useful tools in characterizing quantum phase transitions that only occur, in principle, at the unattainable absolute zero temperature. We first review some interesting results about the behavior of thermal quantum discord for small spin-1/2 chains and show that they already give us important hints of the infinite chain behavior. We then study in detail and in the thermodynamic limit (infinite chains) the thermal quantum correlations for the XXZ and XY models, where one can clearly appreciate that the behavior of thermal quantum discord at finite T is a useful tool to spotlight the critical point of a quantum phase transition.
In this work we use the algebraic Bethe ansatz to derive the general scalar product in the six-vertex model for generic Boltzmann weights. We performed this calculation using only the unitarity property, the Yang-Baxter algebra and the Yang-Baxter equation. We have derived a recurrence relation for the scalar product. The solution of this relation was written in terms of the domain wall partition functions. By its turn, these partition functions were also obtained for generic Boltzmann weights, which provided us with an explicit expression for the general scalar product.
We extend the program initiated in [T. Werlang et al., Phys. Rev. Lett. 105, 095702 (2010)] in several directions. Firstly, we investigate how useful quantum correlations, such as entanglement and quantum discord, are in the detection of critical points of quantum phase transitions when the system is at finite temperatures. For that purpose we study several thermalized spin models in the thermodynamic limit, namely, the XXZ model, the XY model, and the Ising model, all of which with an external magnetic field. We compare the ability of quantum discord, entanglement, and some thermodynamic quantities to spotlight the quantum critical points for several different temperatures. Secondly, for some models we go beyond nearest-neighbors and also study the behavior of entanglement and quantum discord for second nearest-neighbors around the critical point at finite temperature. Finally, we furnish a more quantitative description of how good all these quantities are in spotlighting critical points of quantum phase transitions at finite T, bridging the gap between experimental data and those theoretical descriptions solely based on the unattainable absolute zero assumption.
We study the magnetocaloric effect for the integrable antiferromagnetic high-spin chain. We present an exact computation of the Grüneisen parameter, which is closely related to the magnetocaloric effect, for the quantum spin-s chain on the thermodynamical limit by means of Bethe ansatz techniques and the quantum transfer matrix approach. We have also calculated the entropy S and the isentropes in the (H,T) plane. We have been able to identify the quantum critical points H_c^{(s)}=2/(s+1/2) looking at the isentropes and/or the characteristic behaviour of the Grüneisen parameter.
We compute the quantum correlation (quantum discord (QD)) and the entanglement (EoF) between nearest neighbor qubits (spin-1/2) in an infinite chain described by the Heisenberg model (XXZ Hamiltonian) at finite temperatures. The chain is in the thermodynamic limit and thermalized with a reservoir at temperature T (canonical ensemble). We show that QD, in contrast to EoF and other thermodynamic quantities, spotlight the critical points associated to quantum phase transitions (QPT) for this model even at finite T. This remarkable property of QD may have important implications for experimental characterization of QPTs when one is unable to reach temperatures below which a QPT can be seen.
We study a class of integrable alternating (S1,S2) quantum spin chains with critical ground state properties. Our main result is the description of the thermal Drude weight of the one-dimensional alternating spin chain as a function of temperature. We have identified the thermal current of the model with alternating spins as one of the conserved currents underlying the integrability. This allows for the derivation of a finite set of non-linear integral equations for the thermal conductivity. Numerical solutions to the integral equations are presented for specific cases of the spins S1 and S2. In the low-temperature limit a universal picture evolves where the thermal Drude weight is proportional to temperature T and central charge c.
We consider integrable quantum spin chains with alternating spins (S_1,S_2). We derive a finite set of non-linear integral equations for the thermodynamics of these models by use of the quantum transfer matrix approach. Numerical solutions of the integral equations are provided for quantities like specific heat, magnetic susceptibility and in the case S_1=S_2 for the thermal Drude weight. At low temperatures one class of models shows finite magnetization and the other class presents antiferromagnetic behaviour. The thermal Drude weight behaves linearly on T at low temperatures and is proportional to the central charge c of the system. Quite generally, we observe residual entropy for S_1\neq S_2.
We construct commuting transfer matrices for models describing the interaction between a single quantum spin and a single bosonic mode using the quantum inverse scattering framework. The transfer matrices are obtained from certain inhomogeneous rational vertex models combining bosonic and spin representations of SU(2), subject to non-diagonal toroidal and open boundary conditions. Only open boundary conditions are found to lead to integrable Hamiltonians combining both rotating and counter-rotating terms in the interaction. If the boundary matrices can be brought to triangular form simultaneously, the spectrum of the model can be obtained by means of the algebraic Bethe ansatz after a suitable gauge transformation; the corresponding Hamiltonians are found to be non-hermitian. Alternatively, a certain quasi-classical limit of the transfer matrix is considered where hermitian Hamiltonians are obtained as members of a family of commuting operators; their diagonalization, however, remains an unsolved problem.
We diagonalize the transfer matrix of a solvable vertex model constructed by combining the vector representation of U_q[Sl(n|m)] and its dual by means of the quantum inverse scattering framework. The algebraic Bethe ansatz solution consider all (n+m)!/(n!m!) possibilities of choosing the grading for arbitrary values of n and m. This allows us to derive the transfer matrix eigenvalues and the respective Bethe ansatz equations for general grading choices.
We consider the algebraic Bethe ansatz solution of the integrable and isotropic XXX-S Heisenberg chain with non-diagonal open boundaries. We show that the corresponding K-matrices are similar to diagonal matrices with the help of suitable transformations independent of the spectral parameter. When the boundary parameters satisfy certain constraints we are able to formulate the diagonalization of the associated double-row transfer matrix by means of the quantum inverse scattering method. This allows us to derive explicit expressions for the eigenvalues and the corresponding Bethe ansatz equations. We also present evidences that the eigenvectors can be build up in terms of multiparticle states for arbitrary S.
We consider the quantum inverse scattering method for several mixed integrable models based on the rational SU(N) R-matrix with general toroidal boundary conditions. This includes systems whose Hilbert spaces are invariant by the discrete representations of the group SU(2) and the non-compact group SU(1,1) as well as the conjugate representation of the SU(N) symmetry. Introducing certain transformations on the quantum spaces we are able to solve generalizaed impurity problems including those related to singular matrices.
We formulate the algebraic Bethe ansatz solution of the SU(N) vertex models with rather general non-diagonal toroidal boundary conditions. The reference states needed in the Bethe ansatz construction are found by performing gauge transformations on the Boltzmann weights in the manner of Baxter [1]. The structure of the transfer matrix eigenvectors consists of multi-particle states over such pseudovacuums and the corresponding eigenvalues depend crucially on the boundary matrix eigenvalues. We also discuss for N=2 the peculiar case of twisted boundaries associated to singular matrices.