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arXiv:2411.09368

Entropy dynamics of the binary bond disordered Heisenberg chain

Di Han, Bai, Yankui, Zhao, Yang

Published Nov 14, 2024• 0 citations
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Abstract

In this article, we study the quench dynamics of the binary bond disordered Heisenberg spin chain. First, we develop a new algorithm, the ancilla TEBD method, which combines the purification technique and the time-evolving block decimation (TEBD) algorithm to study the entanglement dynamics of binary bonded disordered spin chains. With the support of exact diagonalization (ED), we calculate the multifaractal dimension of the binary bond disordered Heisenberg spin model and study its dependence on the strength of the disorder potential; we find that the multifaractal dimension shows no critical behavior which rules out the existence of the many body localization transition. Then, we reproduce the long time scaling of the von Neumann entropy at the time scale that is beyond the reach of typical TEBD and time dependent density matrix renormalization group (tDMRG) algorithms. Based on the numerical analysis, we propose that such a long time scaling is due to the competition of the spin interaction and the disorder which can be seen as a new mechanism for the generating of long time scale entropy dynamics. At last, we numerically proved the existence of the transient Mpemba effect in the bond disordered Heisenberg chain.

DOI
10.48550/arxiv.2411.09368

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In this article, we study the quench dynamics of the binary bond disordered Heisenberg spin chain. First, we develop a new algorithm, the ancilla TEBD method, which combines the purification technique and the time-evolving block decimation (TEBD) algorithm to study the entanglement dynamics of binary bonded disordered spin chains. With the support of exact diagonalization (ED), we calculate the multifaractal dimension of the binary bond disordered Heisenberg spin model and study its dependence on the strength of the disorder potential; we find that the multifaractal dimension shows no critical behavior which rules out the existence of the many body localization transition. Then, we reproduce the long time scaling of the von Neumann entropy at the time scale that is beyond the reach of typical TEBD and time dependent density matrix renormalization group (tDMRG) algorithms. Based on the numerical analysis, we propose that such a long time scaling is due to the competition of the spin interaction and the disorder which can be seen as a new mechanism for the generating of long time scale entropy dynamics. At last, we numerically proved the existence of the transient Mpemba effect in the bond disordered Heisenberg chain.
We numerically investigate the growth of the entanglement entropy Sent(t){S}_{\mathrm{ent}}(t)Sent​(t) in time ttt, after a global quench from a product state, in quantum chains with various kinds of disorder. The main focus is, in particular, on fermionic chains with bond disorder. In the noninteracting case at criticality we numerically test recent predictions by the real-space renormalization group for the entanglement growth in time, the maximal entanglement as a function of block size, and the decay of a density-wave order parameter. We show that multiprecision calculations are required to reach the scaling regime and perform such calculations for specific cases. For interacting models with binary bond disorder we present data based on infinite-size density matrix renormalization group calculations and exact diagonalizations. We obtain numerical evidence of a many-body localized phase in bond-disordered systems where ${S}_{\mathrm{ent}}(t)\ensuremath{\sim}lnt$ seems to hold. Our results for bond disorder are contrasted with the well-studied case of potential disorder.
The nonequilibrium dynamics of disordered many-body quantum systems after a quantum quench unveils important insights about the competition between interactions and disorder, yielding, in particular, an interesting perspective toward the understanding of many-body localization. Still, the experimentally relevant effect of bond randomness in long-range interacting spin chains on their dynamical properties have so far not been investigated. In this Letter, we examine the entanglement entropy growth after a global quench in a quantum spin chain with randomly placed spins and long-range tunable interactions decaying with distance with power $\ensuremath{\alpha}$. Using a dynamical version of the strong disorder renormalization group we find for $\ensuremath{\alpha}>{\ensuremath{\alpha}}_{c}$ that the entanglement entropy grows logarithmically with time and becomes smaller with larger $\ensuremath{\alpha}$ as $S(t)={S}_{p}ln(t)/(2\ensuremath{\alpha})$. Here, ${S}_{p}=2ln2\ensuremath{-}1$. We present results of numerical exact diagonalization calculations for system sizes up to $N\ensuremath{\sim}16$ spins, in good agreement with the analytical results for sufficiently large $\ensuremath{\alpha}>{\ensuremath{\alpha}}_{c}\ensuremath{\approx}1.8$. For $\ensuremath{\alpha}<{\ensuremath{\alpha}}_{c}$, we find that the entanglement entropy grows as a power law with time, $S(t)\ensuremath{\sim}{t}^{\ensuremath{\gamma}(\ensuremath{\alpha})}$ with $0<\ensuremath{\gamma}(\ensuremath{\alpha})<1$ a decaying function of the interaction exponent $\ensuremath{\alpha}$.
The non-equilibrium dynamics of disordered many-body quantum systems after a global quantum quench unveils important insights about the competition between interactions and disorder, yielding in particular an insightful perspective on many body localization (MBL). Still, the experimentally relevant effect of bond randomness in long-range interacting spin chains on the quantum quench dynamics have so far not been investigated. In this letter, we examine the entanglement entropy growth after a global quench in a quantum spin chain with randomly placed spins and long-range tunable interactions decaying with distance with power ααα. Using a dynamical version of the strong disorder renormalization group (SDRG) we find for α>αcα>α_cα>αc​ that the entanglement entropy grows logarithmically with time and becomes smaller with larger ααα as S(t)=Spln⁡(t)/(2α)S(t) = S_p \ln(t)/(2α)S(t)=Sp​ln(t)/(2α). Here, Sp=2ln⁡2−1S_p= 2 \ln2 -1Sp​=2ln2−1. We use numerical exact diagonalization (ED) simulations to verify our results for system sizes up to $ N\sim 16$ spins, yielding good agreement for sufficiently large α>αc≈1.8α> α_c \approx 1.8α>αc​≈1.8. For α<αcα<α_cα<αc​, we find that the entanglement entropy grows as a power-law with time, S(t)∼tγ(α)S(t)\sim t^{γ(α)}S(t)∼tγ(α) with 0<γ(α)<10<γ(α)<10<γ(α)<1 a decaying function of the interaction exponent ααα.
By means of the time dependent density matrix renormalization group algorithm we study the zero-temperature dynamics of the Von Neumann entropy of a block of spins in a Heisenberg chain after a sudden quench in the anisotropy parameter. In the absence of any disorder the block entropy increases linearly with time and then saturates. We analyse the velocity of propagation of the entanglement as a function of the initial and final anisotropies and compare our results, wherever possible, with those obtained by means of conformal field theory. In the disordered case we find a slower (logarithmic) evolution which may signal the onset of entanglement localization.
Disorder free many-body localization (MBL) can occur in interacting systems that can dynamically generate their own disorder. We address the thermal-MBL phase transition of two isotropic Heisenberg spin chains that are quasiperiodically coupled to each other. The spin chains are incommensurate and are coupled through a short-range exchange interaction of the X X Z type that decays exponentially with the distance. Using exact diagonalization, matrix product states, and a density matrix renormalization group, we calculate the time evolution of the entanglement entropy at long times and extract the inverse participation ratio in the thermodynamic limit. We show that this system has a robust MBL phase. We establish the phase diagram with the onset of MBL as a function of the interchain exchange coupling and of the incommensuration between the spin chains. The Ising limit of the interchain interaction optimizes the stability of the MBL phase over a broad range of incommensurations above a given critical exchange coupling. Incorporation of interchain spin flips significantly enhances entanglement between the spin chains and produces delocalization, favoring a prethermal phase whose entanglement entropy grows logarithmically with time. Published by the American Physical Society 2024
Abstract. We study the out-of-equilibrium time evolution after a local quench connecting two anisotropic spin-1/2 XXZ Heisenberg open chains via an impurity bond. The dynamics is obtained by means of the adaptive time-dependent density-matrix renormalization group. We show that the entanglement entropies (Von Neumann and Rényi), in the presence of a weakened bond depend on the sign of the bulk interaction. For attractive interaction ( ∆ < 0), the defect turns out to be irrelevant and the evolution is asymptotically equivalent to the one without defect obtained by conformal field theory. For repulsive interaction ( ∆> 0), the defect is relevant and the entanglement saturates to a finite value. This out-of-equilibrium behavior generalizes the well known results for the ground-state entanglement entropy of the model. 1.