Estudo de cadeias quânticas de Heisenberg desordenadas com acoplamentos aperiódicos

We investigate the low-temperature properties of the one-dimensional spin-1 Heisenberg model with geometric fluctuations induced by aperiodic but deterministic coupling distributions, involving two parameters. We focus on two aperiodic sequences, the Fibonacci sequence and the 6-3 sequence. Our goal is to understand how these geometric fluctuations modify the physics of the (gapped) Haldane phase, which corresponds to the ground state of the uniform spin-1 chain. We make use of different adaptations of the strong-disorder renormalization-group (SDRG) scheme of Ma, Dasgupta, and Hu, widely employed in the study of random spin chains, supplemented by quantum Monte Carlo and density-matrix renormalization-group numerical calculations, to study the nature of the ground state as the coupling modulation is increased. We find no phase transition for the Fibonacci chain, while we show that the 6-3 chain exhibits a phase transition to a gapless, aperiodicity-dominated phase similar to the one found for the aperiodic spin-1/2 XXZ chain. Contrary to what is verified for random spin-1 chains, we show that different adaptations of the SDRG scheme may lead to different qualitative conclusions about the nature of the ground state in the presence of aperiodic coupling modulations.We investigate the low-temperature properties of the one-dimensional spin-1 Heisenberg model with geometric fluctuations induced by aperiodic but deterministic coupling distributions, involving two parameters. We focus on two aperiodic sequences, the Fibonacci sequence and the 6-3 sequence. Our goal is to understand how these geometric fluctuations modify the physics of the (gapped) Haldane phase, which corresponds to the ground state of the uniform spin-1 chain. We make use of different adaptations of the strong-disorder renormalization-group (SDRG) scheme of Ma, Dasgupta, and Hu, widely employed in the study of random spin chains, supplemented by quantum Monte Carlo and density-matrix renormalization-group numerical calculations, to study the nature of the ground state as the coupling modulation is increased. We find no phase transition for the Fibonacci chain, while we show that the 6-3 chain exhibits a phase transition to a gapless, aperiodicity-dominated phase similar to the one found for the aperiodic spin-1/2 XXZ chain. Contrary to what is verified for random spin-1 chains, we show that different adaptations of the SDRG scheme may lead to different qualitative conclusions about the nature of the ground state in the presence of aperiodic coupling modulations.

arXiv:1311.5861Physical Review BApr 14, 201413 citations

Aperiodic quantumXXZchains: Renormalization-group results

André P. Vieira

We report a comprehensive investigation of the low-energy properties of antiferromagnetic quantum XXZ spin chains with aperiodic couplings. We use an adaptation of the Ma-Dasgupta-Hu renormalization-group method to obtain analytical and numerical results for the low-temperature thermodynamics and the ground-state correlations of chains with couplings following several two-letter aperiodic sequences, including the quasiperiodic Fibonacci and other precious-mean sequences, as well as sequences inducing strong geometrical fluctuations. For a given aperiodic sequence, we argue that in the easy-plane anisotropy regime, intermediate between the XX and Heisenberg limits, the general scaling form of the thermodynamic properties is essentially given by the exactly known XX behavior, providing a classification of the effects of aperiodicity on XXZ chains. We also discuss the nature of the ground-state structures and their comparison with the random-singlet phase characteristic of random-bond chains.We report a comprehensive investigation of the low-energy properties of antiferromagnetic quantum XXZ spin chains with aperiodic couplings. We use an adaptation of the Ma-Dasgupta-Hu renormalization-group method to obtain analytical and numerical results for the low-temperature thermodynamics and the ground-state correlations of chains with couplings following several two-letter aperiodic sequences, including the quasiperiodic Fibonacci and other precious-mean sequences, as well as sequences inducing strong geometrical fluctuations. For a given aperiodic sequence, we argue that in the easy-plane anisotropy regime, intermediate between the XX and Heisenberg limits, the general scaling form of the thermodynamic properties is essentially given by the exactly known XX behavior, providing a classification of the effects of aperiodicity on XXZ chains. We also discuss the nature of the ground-state structures and their comparison with the random-singlet phase characteristic of random-bond chains.

arXiv:cond-mat/0410747Physical Review BApr 12, 200535 citations

Low-Energy Properties of Aperiodic Quantum Spin Chains

André P. Vieira

We investigate the low-energy properties of antiferromagnetic quantum XXZ spin chains with couplings following two-letter aperiodic sequences, by an adaptation of the Ma-Dasgupta-Hu renormalization-group method. For a given aperiodic sequence, we argue that, in the easy-plane anisotropy regime, intermediate between the XX and Heisenberg limits, the general scaling form of the thermodynamic properties is essentially given by the exactly known XX behavior, providing a classification of the effects of aperiodicity on XXZ chains. As representative illustrations, we present analytical and numerical results for the low-temperature thermodynamics and the ground-state correlations for couplings following the Fibonacci quasiperiodic structure and a binary Rudin-Shapiro sequence, whose geometrical fluctuations are similar to those induced by randomness.We investigate the low-energy properties of antiferromagnetic quantum XXZ spin chains with couplings following two-letter aperiodic sequences, by an adaptation of the Ma-Dasgupta-Hu renormalization-group method. For a given aperiodic sequence, we argue that, in the easy-plane anisotropy regime, intermediate between the XX and Heisenberg limits, the general scaling form of the thermodynamic properties is essentially given by the exactly known XX behavior, providing a classification of the effects of aperiodicity on XXZ chains. As representative illustrations, we present analytical and numerical results for the low-temperature thermodynamics and the ground-state correlations for couplings following the Fibonacci quasiperiodic structure and a binary Rudin-Shapiro sequence, whose geometrical fluctuations are similar to those induced by randomness.

arXiv:cond-mat/0403635Physical Review LettersFeb 22, 200546 citations

Strong-disorder renormalization group study of aperiodic quantum Ising chains

Fleury J Oliveira Filho, Maicon S Faria, André P. Vieira

We employ an adaptation of a strong-disorder renormalization group technique in order to analyze the ferro–paramagnetic quantum phase transition of Ising chains with aperiodic but deterministic couplings under the action of a transverse field. In the presence of marginal or relevant geometric fluctuations induced by aperiodicity, for which the critical behavior is expected to depart from the Onsager universality class, we derive analytical and asymptotically exact expressions for various critical exponents (including the correlation length and the magnetization exponents, which are not easily obtainable by other methods), and shed light onto the nature of the ground-state structures in the neighborhood of the critical point. The main results obtained by this approach are confirmed by finite-size scaling analyses of numerical calculations based on the free-fermion method.We employ an adaptation of a strong-disorder renormalization group technique in order to analyze the ferro–paramagnetic quantum phase transition of Ising chains with aperiodic but deterministic couplings under the action of a transverse field. In the presence of marginal or relevant geometric fluctuations induced by aperiodicity, for which the critical behavior is expected to depart from the Onsager universality class, we derive analytical and asymptotically exact expressions for various critical exponents (including the correlation length and the magnetization exponents, which are not easily obtainable by other methods), and shed light onto the nature of the ground-state structures in the neighborhood of the critical point. The main results obtained by this approach are confirmed by finite-size scaling analyses of numerical calculations based on the free-fermion method.

arXiv:1112.5141Journal of Statistical Mechanics Theory and ExperimentMar 12, 201212 citations

Disorder-induced phases in the S=1 antiferromagnetic Heisenberg chain

Péter Lajkó, Enrico Carlon, Heiko Rieger +1 more

We use extensive density matrix renormalization group (DMRG) calculations to explore the phase diagram of the random $S=1$ antiferromagnetic Heisenberg chain with a power-law distribution of the exchange couplings. We use open chains and monitor the lowest gaps, the end-to-end correlation function and the string order parameter. For this distribution at weak disorder, the system is in the gapless Haldane phase with a disorder dependent dynamical exponent, $z$ , and $z=1$ signals the border between the nonsingular and singular regions of the local susceptibility. For strong enough disorder, which approximately corresponds to a uniform distribution, a transition into the random singlet phase is detected, at which the string order parameter as well as the average end-to-end correlation function are vanishing and at the same time the dynamical exponent is divergent. Singularities of physical quantities are found to be somewhat different in the random singlet phase and in the critical point.We use extensive density matrix renormalization group (DMRG) calculations to explore the phase diagram of the random $S=1$ antiferromagnetic Heisenberg chain with a power-law distribution of the exchange couplings. We use open chains and monitor the lowest gaps, the end-to-end correlation function and the string order parameter. For this distribution at weak disorder, the system is in the gapless Haldane phase with a disorder dependent dynamical exponent, $z$, and $z=1$ signals the border between the nonsingular and singular regions of the local susceptibility. For strong enough disorder, which approximately corresponds to a uniform distribution, a transition into the random singlet phase is detected, at which the string order parameter as well as the average end-to-end correlation function are vanishing and at the same time the dynamical exponent is divergent. Singularities of physical quantities are found to be somewhat different in the random singlet phase and in the critical point.

arXiv:cond-mat/0509646Physical Review BSep 19, 200514 citations

Contribution à l’étude des chaînes de spin quantique avec une perturbation aléatoire ou apériodique

Dimitrios Voliotis

In the present thesis, the critical and off-critical behaviors of quantum spin chains in presence of a random or an aperiodic perturbation of the couplings is studied. The critical behavior of the Ising and Potts random quantum chains is known to be governed by the same Infinite-Disorder Fixed Point. We have implemented a numerical version of the Strong-Disorder Renormalization Group (SDRG) to test this prediction. We then studied the quantum random Ashkin-Teller chain by Density Matrix Renormalization Group. The phase diagram, previously obtained by SDRG, is confirmed by estimating the location of the peaks of the integrated autocorrelation times of both the spin-spin and polarization-polarization autocorrelation functions and of the disorder fluctuations of magnetization and polarization. Finally, the existence of a double-Griffiths phase is shown by a detailed study of the decay of the off-critical autocorrelation functions. As expected, a divergence of the dynamical exponent is observed along the two transition lines. In the aperiodic case, we studied both the Ising and Potts quantum chains. Using numerical SDRG, we confirmed the known analytical results for the Ising chains and proposed a new estimate of the magnetic scaling dimension.For the quantum q-state Potts chain, we estimated the magnetic scaling dimension for various aperiodic sequences and showed that it is independent of q for all sequences with a vanishing wandering exponent. However, we observed that the dynamical exponent is finite and increases with the number of states q. In contrast, for the Rudin-Shapiro sequence, the results are compatible with an Infinite-Disorder Fixed Point with a diverging dynamical exponent, equipe de renormalizationIn the present thesis, the critical and off-critical behaviors of quantum spin chains in presence of a random or an aperiodic perturbation of the couplings is studied. The critical behavior of the Ising and Potts random quantum chains is known to be governed by the same Infinite-Disorder Fixed Point. We have implemented a numerical version of the Strong-Disorder Renormalization Group (SDRG) to test this prediction. We then studied the quantum random Ashkin-Teller chain by Density Matrix Renormalization Group. The phase diagram, previously obtained by SDRG, is confirmed by estimating the location of the peaks of the integrated autocorrelation times of both the spin-spin and polarization-polarization autocorrelation functions and of the disorder fluctuations of magnetization and polarization. Finally, the existence of a double-Griffiths phase is shown by a detailed study of the decay of the off-critical autocorrelation functions. As expected, a divergence of the dynamical exponent is observed along the two transition lines. In the aperiodic case, we studied both the Ising and Potts quantum chains. Using numerical SDRG, we confirmed the known analytical results for the Ising chains and proposed a new estimate of the magnetic scaling dimension.For the quantum q-state Potts chain, we estimated the magnetic scaling dimension for various aperiodic sequences and showed that it is independent of q for all sequences with a vanishing wandering exponent. However, we observed that the dynamical exponent is finite and increases with the number of states q. In contrast, for the Rudin-Shapiro sequence, the results are compatible with an Infinite-Disorder Fixed Point with a diverging dynamical exponent, equipe de renormalization

Dec 5, 20160 citations

We use extensive density matrix renormalization group (DMRG) calculations to explore the phase diagram of the random

S=1

antiferromagnetic Heisenberg chain with a power-law distribution of the exchange couplings. We use open chains and monitor the lowest gaps, the end-to-end correlation function and the string order parameter. For this distribution at weak disorder, the system is in the gapless Haldane phase with a disorder dependent dynamical exponent,

z

, and

z=1

signals the border between the nonsingular and singular regions of the local susceptibility. For strong enough disorder, which approximately corresponds to a uniform distribution, a transition into the random singlet phase is detected, at which the string order parameter as well as the average end-to-end correlation function are vanishing and at the same time the dynamical exponent is divergent. Singularities of physical quantities are found to be somewhat different in the random singlet phase and in the critical point.