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Localização de estados quânticos em cadeias de spins com anisotropia

Márcio Sousa

Published Mar 4, 2024• 0 citations
Publisher

Abstract

The principles of ergodicity and thermalization constitute the foundation of sta- tistical mechanics, stablishing that a many-body system loses progressively its local in- formation as it evolves in time. Nevertheless, these principles can be disrupted when thermalization dynamics lead to the conservation of local information, as observed in the phenomenon known as many-body localization. Quantum spin chains provide a fun- damental platform for exploring the dynamics of closed interacting quantum many-body systems. This study explores the dynamics of a spin chain with ≥ 1/2 within the 1 −2 (or Majumdar-Ghosh) model, incorporating a non-uniform magnetic field and single-ion anisotropy. Employing exact numerical diagonalization, we unveil that a nearly constant- gradient magnetic field suppress thermalization, a phenomenon termed Stark many-body localization (SMBL), previously observed in = 1/2 chains. Furthermore, our findings re- veal that the presence of single-ion anisotropy alone is sufficient to prevent thermalization in the system. Interestingly, when the magnitudes of the magnetic field and anisotropy are comparable, they compete, favoring delocalization. Despite the potential hindrance of SMBL by single-ion anisotropy in this scenario, it introduces an alternative mechanism for localization. Our interpretation, considering local energetic constraints and resonances between degenerate eigenstates, not only provides insights into SMBL but also opens ave- nues for future experimental investigations into the enriched phenomenology of disordered free localized ≥ 1/2 systems.

DOI
10.14393/ufu.di.2024.141

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The principles of ergodicity and thermalization constitute the foundation of sta- tistical mechanics, stablishing that a many-body system loses progressively its local in- formation as it evolves in time. Nevertheless, these principles can be disrupted when thermalization dynamics lead to the conservation of local information, as observed in the phenomenon known as many-body localization. Quantum spin chains provide a fun- damental platform for exploring the dynamics of closed interacting quantum many-body systems. This study explores the dynamics of a spin chain with ≥ 1/2 within the 1 −2 (or Majumdar-Ghosh) model, incorporating a non-uniform magnetic field and single-ion anisotropy. Employing exact numerical diagonalization, we unveil that a nearly constant- gradient magnetic field suppress thermalization, a phenomenon termed Stark many-body localization (SMBL), previously observed in = 1/2 chains. Furthermore, our findings re- veal that the presence of single-ion anisotropy alone is sufficient to prevent thermalization in the system. Interestingly, when the magnitudes of the magnetic field and anisotropy are comparable, they compete, favoring delocalization. Despite the potential hindrance of SMBL by single-ion anisotropy in this scenario, it introduces an alternative mechanism for localization. Our interpretation, considering local energetic constraints and resonances between degenerate eigenstates, not only provides insights into SMBL but also opens ave- nues for future experimental investigations into the enriched phenomenology of disordered free localized ≥ 1/2 systems.
The principles of ergodicity and thermalization constitute the foundation of statistical mechanics, positing that a many-body system progressively loses its local information as it evolves. Nevertheless, these principles can be disrupted when thermalization dynamics lead to the conservation of local information, as observed in the phenomenon known as many-body localization. Quantum spin chains provide a fundamental platform for exploring the dynamics of closed interacting quantum many-body systems. This study explores the dynamics of a spin chain with S≥1/2S\geq 1/2S≥1/2 within the Majumdar-Ghosh model, incorporating a non-uniform magnetic field and single-ion anisotropy. Through the use of exact numerical diagonalization, we unveil that a nearly constant-gradient magnetic field suppress thermalization, a phenomenon termed Stark many-body localization (SMBL), previously observed in S=1/2S=1/2S=1/2 chains. Furthermore, our findings reveal that the sole presence of single-ion anisotropy is sufficient to prevent thermalization in the system. Interestingly, when the magnitudes of the magnetic field and anisotropy are comparable, they compete, favoring delocalization. Despite the potential hindrance of SMBL by single-ion anisotropy in this scenario, it introduces an alternative mechanism for localization. Our interpretation, considering local energetic constraints and resonances between degenerate eigenstates, not only provides insights into SMBL but also opens avenues for future experimental investigations into the enriched phenomenology of disordered free localized S≥1/2S\geq 1/2S≥1/2 systems.
Abstract The principles of ergodicity and thermalization constitute the foundation of statistical mechanics, positing that a many-body system progressively loses its local information as it evolves. Nevertheless, these principles can be disrupted when thermalization dynamics lead to the conservation of local information, as observed in the phenomenon known as many-body localization. Quantum spin chains provide a fundamental platform for exploring the dynamics of closed interacting quantum many-body systems. This study explores the dynamics of a spin chain with S≥1/2S\geq 1/2S≥1/2 within the J1−J2J_1-J_2J1​−J2​, incorporating a non-uniform magnetic field and single-ion anisotropy. Through the use of exact numerical diagonalization, we unveil that a nearly constant-gradient magnetic field suppress thermalization, a phenomenon termed Stark many-body localization (SMBL), previously observed in S=1/2S=1/2S=1/2 chains. Furthermore, our findings reveal that the sole presence of single-ion anisotropy is sufficient to prevent thermalization in the system. Interestingly, when the magnitudes of the magnetic field and anisotropy are comparable, they compete, favoring delocalization. Despite the potential hindrance of SMBL by single-ion anisotropy in this scenario, it introduces an alternative mechanism for localization. Our interpretation, considering local energetic constraints and resonances between degenerate eigenstates, not only provides insights into SMBL but also opens avenues for future experimental investigations into the enriched phenomenology of disordered free localized S≥1/2S\geq 1/2S≥1/2 systems.
Stark many-body localization (SMBL) is a phenomenon observed in interacting systems with a nearly uniform spatial gradient applied field. Contrasting to the traditional many-body localization phenomenon, SMBL does not require disorder. Here we investigate SMBL in a spin-1/21/21/2 described by a Heisenberg model including a next-nearest-neighbor exchange coupling. By employing an exact diagonalization approach and time evolution calculation we analyze both level spacing ratio (LSR) statistics of the Hamiltonian model as well as the dynamics of the system from a given initial state. Our results reveals that for zero field in our finite system, LSR statistics suggest localization while the dynamics shows thermalization, which has been attributed to a finite-size effect. Slightly nonuniform field gradient, LSR statistic predictions agree very well with the dynamics of the physical quantities indicating delocalization and localization for small and large field gradient, respectively. More interestingly, we find that localization is robust in the presence of next-nearest-neighbor coupling in the Hamiltonian. Moreover, this coupling can be tuned to enhance SMBL in the system, meaning that localized regimes can be obtained for smaller field gradient as compared to the traditional nearest-neighbor isotropic Heisenberg model.
Novel paradigms of strong ergodicity breaking have recently attracted significant attention in condensed matter physics. Understanding the exact conditions required for their emergence or breakdown not only sheds more light on thermalization and its absence in closed quantum many-body systems, but it also has potential benefits for applications in quantum information technology. A case of particular interest is many-body localization whose conditions are not yet fully settled. Here, we prove that spin chains symmetric under a combination of mirror and spin-flip symmetries and with a non-degenerate spectrum show finite spin transport at zero total magnetization and infinite temperature. We demonstrate this numerically using two prominent examples: the Stark many-body localization system (Stark-MBL) and the symmetrized many-body localization system (symmetrized-MBL). We provide evidence of delocalization at all energy densities and show that delocalization persists when the symmetry is broken. We use our results to construct two localized systems which, when coupled, delocalize each other. Our work demonstrates the dramatic effect symmetries can have on disordered systems, proves that the existence of exact resonances is not a sufficient condition for delocalization, and opens the door to generalization to higher spatial dimensions and different conservation laws.
In this work we demonstrate that nonrandom mechanisms that lead to single-particle localization may also lead to many-body localization, even in the absence of disorder. In particular, we consider interacting spins and fermions in the presence of a linear potential. In the noninteracting limit, these models show the well-known Wannier-Stark localization. We analyze the fate of this localization in the presence of interactions. Remarkably, we find that beyond a critical value of the potential gradient these models exhibit nonergodic behavior as indicated by their spectral and dynamical properties. These models, therefore, constitute a class of generic nonrandom models that fail to thermalize. As such, they suggest new directions for experimentally exploring and understanding the phenomena of many-body localization. We supplement our work by showing that by using machine-learning techniques the level statistics of a system may be calculated without generating and diagonalizing the Hamiltonian, which allows a generation of large statistics.
Thermalization in many-body systems can be inhibited by the application of a linearly increasing potential, which is known as Stark many-body localization. Here we investigate the fate of this phenomenon on a two-dimensional disorder-free lattice with up to $24\ifmmode\times\else\texttimes\fi{}6$ sites. Similar to the one-dimensional case, ``density-polarized'' regions can act as bottlenecks for transport and thermalization on laboratory timescales. However, compared to the one-dimensional case, a substantially stronger potential gradient is needed to prevent thermalization when an extra spatial dimension is involved. The origin of this difference and implications for experiments are discussed. We argue that delocalization is generally favored for typical states in two-dimensional Stark many-body systems, although nonergodicity can still be observed for a specific choice of initial states, such as those probed in experiments.