اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدWeak-ergodicity-breaking via lattice supersymmetry
76
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study the spectral properties of $D$-dimensional $N=2$ supersymmetric lattice models. We find systematic departures from the eigenstate thermalization hypothesis (ETH) in the form of a degenerate set of ETH-violating supersymmetric (SUSY) doublets, also referred to as many-body scars, that we construct analytically. These states are stable against arbitrary SUSY-preserving perturbations, including inhomogeneous couplings. For the specific case of two-leg ladders, we provide extensive numerical evidence that shows how those states are the only ones violating the ETH, and discuss their robustness to SUSY-violating perturbations. Our work suggests a generic mechanism to stabilize quantum many-body scars in lattice models in arbitrary dimensions.
قيم البحث
اقرأ أيضاً
We introduce and analyze a quantum spin/Majorana chain with a tricritical Ising point separating a critical phase from a gapped phase with order-disorder coexistence. We show that supersymmetry is not only an emergent property of the scaling limit, b
ut manifests itself on the lattice. Namely, we find explicit lattice expressions for the supersymmetry generators and currents. Writing the Hamiltonian in terms of these generators allows us to find the ground states exactly at a frustration-free coupling. These confirm the coexistence between two (topologically) ordered ground states and a disordered one in the gapped phase. Deforming the model by including explicit chiral symmetry breaking, we find the phases persist up to an unusual chiral phase transition where the supersymmetry becomes exact even on the lattice.
Statistical analysis of the eigenfunctions of the Anderson tight-binding model with on-site disorder on regular random graphs strongly suggests that the extended states are multifractal at any finite disorder. The spectrum of fractal dimensions $f(al
pha)$ defined in Eq.(3), remains positive for $alpha$ noticeably far from 1 even when the disorder is several times weaker than the one which leads to the Anderson localization, i.e. the ergodicity can be reached only in the absence of disorder. The one-particle multifractality on the Bethe lattice signals on a possible inapplicability of the equipartition law to a generic many-body quantum system as long as it remains isolated.
Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is connected with no
n-ergodic behaviour. In such cases the time averages remain random variables and hence irreproducible. Here we present a detailed analysis of the time averaged mean squared displacement for systems governed by anomalous diffusion, considering both unconfined and restricted (corralled) motion. We discuss the behaviour of the time averaged mean squared displacement for two prominent stochastic processes, namely, continuous time random walks and fractional Brownian motion. We also study the distribution of the time averaged mean squared displacement around its ensemble mean, and show that this distribution preserves typical process characteristic even for short time series. Recently, velocity correlation functions were suggested to distinguish between these processes. We here present analytucal expressions for the velocity correlation functions. Knowledge of the results presented here are expected to be relevant for the correct interpretation of single particle trajectory data in complex systems.
We construct topological defects in two-dimensional classical lattice models and quantum chains. The defects satisfy local commutation relations guaranteeing that the partition function is independent of their path. These relations and their solution
s are extended to allow defect lines to fuse, branch and satisfy all the properties of a fusion category. We show how the two-dimensional classical lattice models and their topological defects are naturally described by boundary conditions of a Turaev-Viro-Barrett-Westbury partition function. These defects allow Kramers-Wannier duality to be generalized to a large class of models, explaining exact degeneracies between non-symmetry-related ground states as well as in the low-energy spectrum. They give a precise and general notion of twisted boundary conditions and the universal behaviour under Dehn twists. Gluing a topological defect to a boundary yields linear identities between partition functions with different boundary conditions, allowing ratios of the universal g-factor to be computed exactly on the lattice. We develop this construction in detail in a variety of examples, including the Potts, parafermion and height models.
In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect commutatio
n relations, cousins of the Yang-Baxter equation. These relations and their solutions can be extended to allow defect lines to branch and fuse, again with properties depending only on topology. In this part I, we focus on the simplest example, the Ising model. We define lattice spin-flip and duality defects and their branching, and prove they are topological. One useful consequence is a simple implementation of Kramers-Wannier duality on the torus and higher genus surfaces by using the fusion of duality defects. We use these topological defects to do simple calculations that yield exact properties of the conformal field theory describing the continuum limit. For example, the shift in momentum quantization with duality-twisted boundary conditions yields the conformal spin 1/16 of the chiral spin field. Even more strikingly, we derive the modular transformation matrices explicitly and exactly.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
