arXiv subjects

J. C. Xavier

Publications and source records attributed to J. C. Xavier.

At least 19 recordsLinked to original sources

arXiv2026

Dynamic quantum phase transitions in the two-leg Creutz ladder with long-range hopping

In this work, we investigate quantum quenches in the two-leg Creutz model with long-range hopping, where the hopping amplitudes decay with distance as a power law characterized by an exponent $\nu$ and have a finite range $D$. We first obtain the exact solution of a generic two-band model in momentum space. This allows us to compute the Loschmidt amplitude and, consequently, the dynamical free energy $f(\texttt{t})$ of the two-band model. We also show how to determine the Yang-Lee Fisher (YLF) zeros by solving a nonlinear equation. We demonstrate that the two-leg Creutz model in momentum space is a special case of the generic two-band model. Using these results, we identify the non-analyticities in the dynamical free energy $f(\texttt{t})$ at critical times $\texttt{t}_{c}$. We find that the number of nontrivial critical times $N_{s}$ depends on both $\nu$ and $D$. In particular, we show that for small $\nu$ and large $D$ the critical times become increasingly dense, leading, in the appropriate regime, to non-analyticities at an increasingly dense set of times---similar to what was observed by Xavier and Hoyos [Phys. Rev. B, $\textbf{108}$, 214303 (2023)] in the Su-Schrieffer-Heeger (SSH) model with long-range hopping terms.

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arXiv2023

Effect of long-range hopping on dynamic quantum phase transitions of an exactly solvable free-fermion model: Nonanalyticities at almost all times

In this work, we investigate quenches in a free-fermion chain with long-range hopping which decay with the distance with an exponent $ν$ and has range $D$. By exploring the exact solution of the model, we found that the dynamic free energy is non-analytical, in the thermodynamic limit, whenever the sudden quench crosses the equilibrium quantum critical point. We were able to determine the non-analyticities of dynamic free energy $f(t)$ at some critical times $t^{c}$ by solving nonlinear equations. We also show that the Yang-Lee-Fisher (YLF) zeros cross the real-time axis at those critical times. We found that the number of nontrivial critical times, $N_{s},$ depends on $ν$ and $D$. In particular, we show that for small $ν$ and large $D$ the dynamic free energy presents non-analyticities in any time interval $Δt\sim1/D\ll1$, i.e., there are \emph{non-analyticities at almost all times}. For the spacial case $ν=0$, we obtain the critical times in terms of a simple expression of the model parameters and also show that $f(t)$ is non-analytical even for finite system under anti-periodic boundary condition, when we consider some special values of quench parameters. We also show that, generically, the first derivative of the dynamic free energy is discontinuous at the critical time instant when the YLF zeros are non-degenerate. On the other hand, when they become degenerate, all derivatives of $f(t)$ exist at the associated critical instant.

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arXiv2022

Disorder-induced dynamical Griffiths singularities after certain quantum quenches

We demonstrate that in a class of disordered quantum systems the dynamical partition function is not an analytical function in a time window after certain quantum quenches. We related this behavior to rare and large regions with atypical inhomogeneity configurations. We also quantify the strength of the associated singularities and their signatures in experiments and numerical studies.

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arXiv2021

Coexistence of spontaneous dimerization and magnetic order in a transverse-field Ising ladder with four-spin interactions

The spin-1/2 transverse field two-leg Ising ladder with nearest-neighbor exchange and plaquette four-spin interaction $J_{4}$ is studied analytically and numerically with the density matrix renormalization group approach. The quantum phase diagram in the transverse field $B$ versus $J_{4}$ plane has been obtained. There are three different phases: a paramagnetic (PM) phase for high values of the transverse field and, for low values of $B$, a ferromagnetic (FM) ordered phase for small $J_{4}$ and a dimerized-rung (DR) phase for large negative values of $J_{4}$. All phases are separated by quantum phase transition lines meeting at a multicritical point. The critical lines have been obtained by exploring the entanglement entropy. The results show that along the critical lines the central charge is $c=1/2$, while at the multicritical point one has $c=1$. The scaling dimension of the energy operator is $X_ε=1$, in agreement with the universality class of the critical behavior of the quantum Ising chain. An effective field theory for the multicritical point is also discussed. The FM and the DR order parameters have also been computed and we found a region where the FM and the DR phases coexist.

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arXiv2020

Confinement and bound states of bound states in a transverse-field two-leg Ising ladder

Weakly coupled Ising chains provide a condensed-matter realization of confinement. In these systems, kinks and antikinks bind into mesons due to an attractive interaction potential that increases linearly with the distance between the particles. While single mesons have been directly observed in experiments, the role of the multiparticle continuum and bound states of mesons in the excitation spectrum is far less clear. Using time-dependent density matrix renormalization group methods, we study the dynamical structure factors of one- and two-spin operators in a transverse-field two-leg Ising ladder in the ferromagnetic phase. The propagation of time-dependent correlations and the two-spin excitation spectrum reveal the existence of interchain bound states, which are absent in the one-spin dynamical structure factor. We also identify two-meson bound states that appear at higher energies, above the thresholds of several two-meson continua.

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arXiv2020

Entanglement and boundary entropy in quantum spin chains with arbitrary direction of the boundary magnetic fields

We calculate the entanglement and the universal boundary entropy (BE) in the critical quantum spin chains, such as the transverse field Ising chain and the XXZ chain, with arbitrary direction of the boundary magnetic field (ADBMF). We determine the boundary universality class that an ADBMF induces. In particular, we show that the induced boundary conformal field theory (BCFT) depends on the point on the Bloch sphere where the boundary magnetic field directs. We show that the classification of the directions boils down to the simple fact that the boundary field breaks the bulk symmetry or does not. We present a procedure to estimate the universal BE, based on the finite-size corrections of the entanglement entropy, that apply to the ADBMF. To calculate the universal BE in the XXZ chain, we use the density matrix renormalization group (DMRG). The transverse field XY chain with ADBMF after Jordan-Wigner (JW) transformation is not a quadratic free fermion Hamiltonian. We map this model to a quadratic free fermion chain by introducing two extra ancillary spins coupled to the main chain at the boundaries, which makes the problem {\it{integrable}}. The eigenstates of the transverse field XY chain can be obtained by proper projection in the enlarged chain. Using this mapping, we are able to calculate the entanglement entropy of the transverse field XY chain using the usual correlation matrix technique up to relatively large sizes.

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arXiv2018

Adaptive Density Matrix Renormalization Group for Disordered Systems

We propose a simple modification of the density matrix renormalization group (DMRG) method in order to tackle strongly disordered quantum spin chains. Our proposal, akin to the idea of the adaptive time-dependent DMRG, enables us to reach larger system sizes in the strong disorder limit by avoiding most of the metastable configurations which hinder the performance of the standard DMRG method. We benchmark our adaptive method by revisiting the random antiferromagnetic XXZ spin-1/2 chain for which we compute the random-singlet ground-state average spin-spin correlation functions and von Neumann entanglement entropy. We then apply our method to the bilinear-biquadratic random antiferromagnetic spin-1 chain tuned to the antiferromagnet and gapless highly symmetric SU(3) point. We find the new result that the mean correlation function decays algebraically with the same universal exponent $ϕ=2$ as the spin-1/2 chain. We then perform numerical and analytical strong-disorder renormalization-group calculations which confirm this finding and generalize it for any highly symmetric SU($N$) random-singlet state.

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arXiv2018

Equipartition of the Entanglement Entropy

The entanglement in a quantum system that possess an internal symmetry, characterized by the Sz-magnetization or U(1)-charge, is distributed among different sectors. The aim of this letter is to gain a deeper understanding of the contribution to the entanglement entropy in each of those sectors for the ground state of conformal invariant critical one dimensional systems. We find surprisingly that the entanglement entropy is equally distributed among the different magnetization sectors. Its value is given by the standard area law violating logarithmic term, that depends on the central charge c, minus a double logarithmic correction related to the zero temperature susceptibility. This result provides a new method to estimate simultaneously the central charge c and the critical exponents of U(1)-symmetric quantum chains. The method is numerically simple and gives precise results for the spin-1/2 quantum XXZ chain. We also compute the probability distribution of the magnetization in contiguous sublattices.

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arXiv2016

Boundary versus bulk behavior of time-dependent correlation functions in one-dimensional quantum systems

We study the influence of reflective boundaries on time-dependent responses of one-dimensional quantum fluids at zero temperature beyond the low-energy approximation. Our analysis is based on an extension of effective mobile impurity models for nonlinear Luttinger liquids to the case of open boundary conditions. For integrable models, we show that boundary autocorrelations oscillate as a function of time with the same frequency as the corresponding bulk autocorrelations. This frequency can be identified as the band edge of elementary excitations. The amplitude of the oscillations decays as a power law with distinct exponents at the boundary and in the bulk, but boundary and bulk exponents are determined by the same coupling constant in the mobile impurity model. For nonintegrable models, we argue that the power-law decay of the oscillations is generic for autocorrelations in the bulk, but turns into an exponential decay at the boundary. Moreover, there is in general a nonuniversal shift of the boundary frequency in comparison with the band edge of bulk excitations. The predictions of our effective field theory are compared with numerical results obtained by time-dependent density matrix renormalization group (tDMRG) for both integrable and nonintegrable critical spin-$S$ chains with $S=1/2$, $1$ and $3/2$.

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arXiv2014

Universal Finite-Size Corrections of the Entanglement Entropy of Quantum Ladders and the Entropic Area Law

We investigate the finite-size corrections of the entanglement entropy of critical ladders and propose a conjecture for its scaling behavior. The conjecture is verified for free fermions, Heisenberg and quantum Ising ladders. Our results support that the prefactor of the logarithmic correction of the entanglement entropy of critical ladder models is universal and it is associated with the central charge of the one-dimensional version of the models and with the number of branches associated with gapless excitations. Our results suggest that it is possible to infer whether there is a violation of the entropic area law in two-dimensional critical systems by analyzing the scaling behavior of the entanglement entropy of ladder systems, which are easier to deal.

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arXiv2014

The N-Leg spin-S Heisenberg ladders: A DMRG study

We investigate the N-leg spin-S Heisenberg Ladders by using the density matrix renormalization group method. We present estimates of the spin gap $Δ_{s}$ and of the ground state energy per site $e_{\infty}^{N}$ in the thermodynamic limit for ladders with widths up to six legs and spin $S\leq\frac{5}{2}$. We also estimate the ground state energy per site $e_{\infty}^{2D}$ for the infinite two-dimensional spin-S Heisenberg model. Our results support that for ladders with semi-integer spins the spin excitation is gapless for $N$ odd and gapped for N even. Whereas for integer spin ladders the spin gap is nonzero, independent of the number of legs. Those results agree with the well known conjectures of Haldane and Sénéchal-Sierra for chains and ladders, respectively. We also observe edge states for ladders with $N$ odd, similar to what happens in the integer spin chains.

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arXiv2013

Entanglement Entropies in Conformal Systems with Boundaries

We study the entanglement entropies in one-dimensional open critical systems, whose effective description is given by a conformal field theory with boundaries. We show that for pure-state systems formed by the ground state or by the excited states associated to primary fields, the entanglement entropies have a finite-size behavior that depends on the correlation of the underlying field theory. The analytical results are checked numerically, finding excellent agreement for the quantum chains ruled by the theories with central charge $c=1/2$ and $c=1$.

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arXiv2012

Entanglement Entropy of the Low-Lying Excited States and Critical Properties of an Exactly Solvable Two-Leg Spin Ladder with Three-Spin Interactions

In this work, we investigate an exactly solvable two-leg spin ladder with three-spin interactions. We obtain analytically the finite-size corrections of the low-lying energies and determine the central charge as well as the scaling dimensions. The model considered in this work has the same universality class of critical behavior of the XX chain with central charge c=1. By using the correlation matrix method, we also study the finite-size corrections of the Renyi entropy of the ground state and of the excited states. Our results are in agreement with the predictions of the conformal field theory.

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arXiv2012

Finite-size corrections of the Entanglement Entropy of critical quantum chains

Using the density matrix renormalization group, we calculated the finite-size corrections of the entanglement $α$-Renyi entropy of a single interval for several critical quantum chains. We considered models with U(1) symmetry like the spin-1/2 XXZ and spin-1 Fateev-Zamolodchikov models, as well models with discrete symmetries such as the Ising, the Blume-Capel and the three-state Potts models. These corrections contain physically relevant information. Their amplitudes, that depend on the value of $α$, are related to the dimensions of operators in the conformal field theory governing the long-distance correlations of the critical quantum chains. The obtained results together with earlier exact and numerical ones allow us to formulate some general conjectures about the operator responsible for the leading finite-size correction of the $α$-Renyi entropies. We conjecture that the exponent of the leading finite-size correction of the $α$-Renyi entropies is $p_α=2X_ε/α$ for $α>1$ and $p_{1}=ν$, where $X_ε$ is the dimensions of the energy operator of the model and $ν=2$ for all the models.

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arXiv2011

Precise Determination of Quantum Critical Points by the Violation of the Entropic Area Law

Finite-size scaling analysis turns out to be a powerful tool to calculate the phase diagram as well as the critical properties of two dimensional classical statistical mechanics models and quantum Hamiltonians in one dimension. The most used method to locate quantum critical points is the so called crossing method, where the estimates are obtained by comparing the mass gaps of two distinct lattice sizes. The success of this method is due to its simplicity and the ability to provide accurate results even considering relatively small lattice sizes. In this paper, we introduce an estimator that locates quantum critical points by exploring the known distinct behavior of the entanglement entropy in critical and non critical systems. As a benchmark test, we use this new estimator to locate the critical point of the quantum Ising chain and the critical line of the spin-1 Blume-Capel quantum chain. The tricritical point of this last model is also obtained. Comparison with the standard crossing method is also presented. The method we propose is simple to implement in practice, particularly in density matrix renormalization group calculations, and provides us, like the crossing method, amazingly accurate results for quite small lattice sizes. Our applications show that the proposed method has several advantages, as compared with the standard crossing method, and we believe it will become popular in future numerical studies.

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arXiv2011

Renyi Entropy and Parity Oscillations of the Anisotropic Spin-s Heisenberg Chains in a Magnetic Field

Using the density matrix renormalization group, we investigate the Renyi entropy of the anisotropic spin-s Heisenberg chains in a z-magnetic field. We considered the half-odd integer spin-s chains, with s=1/2,3/2 and 5/2, and periodic and open boundary conditions. In the case of the spin-1/2 chain we were able to obtain accurate estimates of the new parity exponents $p_α^{(p)}$ and $p_α^{(o)}$ that gives the power-law decay of the oscillations of the $α-$Renyi entropy for periodic and open boundary conditions, respectively. We confirm the relations of these exponents with the Luttinger parameter $K$, as proposed by Calabrese et al. [Phys. Rev. Lett. 104, 095701 (2010)]. Moreover, the predicted periodicity of the oscillating term was also observed for some non-zero values of the magnetization $m$. We show that for $s>1/2$ the amplitudes of the oscillations are quite small, and get accurate estimates of $p_α^{(p)}$ and $p_α^{(o)}$ become a challenge. Although our estimates of the new universal exponents $p_α^{(p)}$ and $p_α^{(o)}$ for the spin-3/2 chain are not so accurate, they are consistent with the theoretical predictions.

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arXiv2010

Entanglement Entropy, Conformal Invariance and the Critical Behavior of the Anisotropic Spin-S Heisenberg Chains: A DMRG study

Using the density-matrix renormalization-group, we investigate the critical behavior of the anisotropic Heisenberg chains with spins up to $S=9/2$. We show that through the relations arising from the conformal invariance and the DMRG technique it is possible to obtain accurate finite-size estimates of the conformal anomaly $c$, the sound velocity $v_{s}$, the anomalous dimension $x_{bulk}$, and the surface exponent $x_{s}$ of the anisotropic spin-$S$ Heisenberg chains with relatively good accuracy without fitting parameters. Our results indicate that the entanglement entrop $S(L,l_{A},S)$ of the spin-$S$ Heisenberg chains satisfies the relation $S(L,l_{A},S)-S(L,l_{A},S-1)=1/(2S+1)$ for $S>3/2$ in the thermodynamic limit.

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arXiv2010

Coexistence of Pairing Tendencies and Ferromagnetism in a Doped Two-Orbital Hubbard Model on Two-Leg Ladders

Using the Density Matrix Renormalization Group and two-leg ladders, we investigate an electronic two-orbital Hubbard model including plaquette diagonal hopping amplitudes. Our goal is to search for regimes where charges added to the undoped state form pairs, presumably a precursor of a superconducting state.For the electronic density $ρ=2$, i.e. the undoped limit, our investigations show a robust $(π,0)$ antiferromagnetic ground state, as in previous investigations. Doping away from $ρ=2$ and for large values of the Hund coupling $J$, a ferromagnetic region is found to be stable. Moreover, when the interorbital on-site Hubbard repulsion is smaller than the Hund coupling, i.e. for $U'<J$ in the standard notation of multiorbital Hubbard models, our results indicate the coexistence of pairing tendencies and ferromagnetism close to $ρ=2$. These results are compatible with previous investigations using one dimensional systems. Although further research is needed to clarify if the range of couplings used here is of relevance for real materials, such as superconducting heavy fermions or pnictides, our theoretical results address a possible mechanism for pairing that may be active in the presence of short-range ferromagnetic fluctuations.

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