Level statistics of the disordered Haldane-Shastry model with $1/r^α$ interactionLevel statistics of the disordered Haldane-Shastry model with $1/r^α$ interaction

Vengatesan Ganapathy, Pranay Patil, Ajit C. Balram

Understanding how the interaction range and various types of disorder affect the level statistics of many-body quantum systems, leading to the emergence of many-body localization (MBL), is a challenging open frontier. We study the level statistics of a variant of the spin- $1/2$ Haldane-Shastry model with $1/r^α$ interactions, where $α{\geq}0$ parametrizes the range of the interactions, in the presence of position disorder and/or random magnetic fields. We find that neither position disorder nor random magnetic fields alone yields pristine Poisson statistics in this system; however, Poisson statistics emerge in their combined presence, suggesting the emergence of MBL when both types of disorder coexist. Interestingly, once random magnetic fields break the $SU(2)$ symmetry, the strength of the position disorder, $δ$ , appears to play an important role, as evidenced by an approximate scaling collapse of the disorder-averaged gap ratios that is parametrized in terms of a single parameter, $αδ$ .Understanding how the interaction range and various types of disorder affect the level statistics of many-body quantum systems, leading to the emergence of many-body localization (MBL), is a challenging open frontier. We study the level statistics of a variant of the spin-$1/2$ Haldane-Shastry model with $1/r^α$ interactions, where $α{\geq}0$ parametrizes the range of the interactions, in the presence of position disorder and/or random magnetic fields. We find that neither position disorder nor random magnetic fields alone yields pristine Poisson statistics in this system; however, Poisson statistics emerge in their combined presence, suggesting the emergence of MBL when both types of disorder coexist. Interestingly, once random magnetic fields break the $SU(2)$ symmetry, the strength of the position disorder, $δ$, appears to play an important role, as evidenced by an approximate scaling collapse of the disorder-averaged gap ratios that is parametrized in terms of a single parameter, $αδ$.

cond-mat.str-elCross-listedarXiv:2604.14695Physical review. B./Physical review. BApr 17, 20260 citations

Disordered Haldane-Shastry model

Shriya Pai, N. S. Srivatsa, Anne E. B. Nielsen

The Haldane-Shastry model is one of the most studied interacting spin systems. The Yangian symmetry makes it exactly solvable, and the model has semionic excitations. We introduce disorder into the Haldane-Shastry model by allowing the spins to sit at random positions on the unit circle and study the properties of the eigenstates. At weak disorder, the spectrum is similar to the spectrum of the clean Haldane-Shastry model. At strong disorder, the long-range interactions in the model do not decay as a simple power law. The eigenstates in the middle of the spectrum follow a volume law, but the coefficient is small, and the entropy is hence much less than for an ergodic system. In addition, the energy level spacing statistics is neither Poissonian nor of the Wigner-Dyson type. The behavior at strong disorder hence serves as an example of a nonergodic phase, which is not of the many-body localized kind, in a model with long-range interactions and SU(2) symmetry.The Haldane-Shastry model is one of the most studied interacting spin systems. The Yangian symmetry makes it exactly solvable, and the model has semionic excitations. We introduce disorder into the Haldane-Shastry model by allowing the spins to sit at random positions on the unit circle and study the properties of the eigenstates. At weak disorder, the spectrum is similar to the spectrum of the clean Haldane-Shastry model. At strong disorder, the long-range interactions in the model do not decay as a simple power law. The eigenstates in the middle of the spectrum follow a volume law, but the coefficient is small, and the entropy is hence much less than for an ergodic system. In addition, the energy level spacing statistics is neither Poissonian nor of the Wigner-Dyson type. The behavior at strong disorder hence serves as an example of a nonergodic phase, which is not of the many-body localized kind, in a model with long-range interactions and SU(2) symmetry.

arXiv:2003.12579Physical review. B./Physical review. BJul 8, 20204 citations

Many-body localization in disorder-free systems: The importance of finite-size constraints

Zlatko Papić, E. Miles Stoudenmire, Dmitry A. Abanin

arXiv:1501.00477Annals of PhysicsAug 31, 201596 citations

Many-body Localization Transition of Ising Spin-1 Chains

Taotao Hu, Yining Zhang, Ren, Hang +4 more

In this paper, we theoretically investigate the many-body localization properties of one-dimensional Ising spin-1 chains by using the methods of exact matrix diagonalization. We compare it with the MBL properties of the Ising spin-1/2 chains. The results indicate that the one-dimensional Ising spin-1 chains can also undergo MBL phase transition. There are various forms of disorder, and we compare the effects of different forms of quasi-disorder and random disorder on many-body localization in this paper. First, we calculate the exctied-state fidelity to study the MBL phase transtion. By changing the form of the quasi-disorder, we study the MBL transition of the system with different forms of quasi-disorder and compare them with those of the random disordered system. The results show that both random disorder and quasi-disorder can cause the MBL phase transition in the one-dimensional Ising spin-1 chains. In order to study the effect of spin interactions, we compare Ising spin-1 chains and spin-1/2 chains with the next-nearest-neighbour(N-N) two-body interactions and the next-next-nearest-neighbour (N-N-N)interactions. The results show that the critical point increases with the addition of the interaction. Then we study the dynamical properties of the model by the dynamical behavior of diagonal entropy (DE), local magnetization and the time evolution of fidelity to further prove the occurrence of MBL phase transition in the disordered Ising spin-1 chains with the (N-N) coupling term and distinguish the ergodic phase (thermal phase) and the many-body localized phase. Lastly, we delve into the impact of periodic driving on one-dimensional Ising spin-1 chains. And we compare it with the results obtained from the Ising spin-1/2 chains. It shows that periodic driving can cause Ising spin-1 chains and Ising spin-1/2 chains to occur the MBL transition.In this paper, we theoretically investigate the many-body localization properties of one-dimensional Ising spin-1 chains by using the methods of exact matrix diagonalization. We compare it with the MBL properties of the Ising spin-1/2 chains. The results indicate that the one-dimensional Ising spin-1 chains can also undergo MBL phase transition. There are various forms of disorder, and we compare the effects of different forms of quasi-disorder and random disorder on many-body localization in this paper. First, we calculate the exctied-state fidelity to study the MBL phase transtion. By changing the form of the quasi-disorder, we study the MBL transition of the system with different forms of quasi-disorder and compare them with those of the random disordered system. The results show that both random disorder and quasi-disorder can cause the MBL phase transition in the one-dimensional Ising spin-1 chains. In order to study the effect of spin interactions, we compare Ising spin-1 chains and spin-1/2 chains with the next-nearest-neighbour(N-N) two-body interactions and the next-next-nearest-neighbour (N-N-N)interactions. The results show that the critical point increases with the addition of the interaction. Then we study the dynamical properties of the model by the dynamical behavior of diagonal entropy (DE), local magnetization and the time evolution of fidelity to further prove the occurrence of MBL phase transition in the disordered Ising spin-1 chains with the (N-N) coupling term and distinguish the ergodic phase (thermal phase) and the many-body localized phase. Lastly, we delve into the impact of periodic driving on one-dimensional Ising spin-1 chains. And we compare it with the results obtained from the Ising spin-1/2 chains. It shows that periodic driving can cause Ising spin-1 chains and Ising spin-1/2 chains to occur the MBL transition.

arXiv:2405.02028May 3, 20240 citations

Level statistics of the disordered Haldane-Shastry model with

1/r^α

interaction

1/2

Haldane-Shastry model with

1/r^α

interactions, where

α{\geq}0

parametrizes the range of the interactions, in the presence of position disorder and/or random magnetic fields. We find that neither position disorder nor random magnetic fields alone yields pristine Poisson statistics in this system; however, Poisson statistics emerge in their combined presence, suggesting the emergence of MBL when both types of disorder coexist. Interestingly, once random magnetic fields break the

SU(2)

symmetry, the strength of the position disorder,

δ

, appears to play an important role, as evidenced by an approximate scaling collapse of the disorder-averaged gap ratios that is parametrized in terms of a single parameter,

αδ