Explicit construction of local conserved operators in disordered many-body systems

O’Brien, Thomas E.; Abanin, Dmitry A.; Vidal, Guifré; Papić, Zlatko

doi:10.1103/physrevb.94.144208

Cited by 53 publications

(51 citation statements)

References 40 publications

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“…In this case we rely on a method developed to construct conserved operators called "l-bits" for a many-body localized system [26,27]. The construction of these conserved quantities from first principles is difficult, but algorithms which can construct them using various methods do exist [28][29][30][31][32][33][34][35][36][37][38][39][40].…”

Section: Edge Mode Constructionmentioning

confidence: 99%

Edge mode locality in perturbed symmetry protected topological order

et al. 2019

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Spin chains with a symmetry-protected edge zero modes can be seen as prototypical systems for exploring topological signatures in quantum systems. However in an experimental realization of such a system, spurious interactions may cause the edge zero modes to delocalize. To combat this influence beyond simply increasing the bulk gap, it has been proposed to harness disorder which does not drive the system out of a topological phase. Equipped with numerical tools for constructing locally conserved operators that we introduce, we comprehensively explore the interplay of local interactions and disorder on localized edge modes in such systems. Contrary to established heuristic reasoning, we find that disorder has no effect on the edge mode localization length in the non-interacting regime. Moreover, disorder helps localize only a subset of edge modes in the truly interacting regime. We identify one edge mode operator that behaves as if subjected to a non-interacting perturbation, i.e., shows no disorder dependence. This implies that in finite systems, edge mode operators effectively delocalize at distinct interaction strengths despite the presence of disorder. In essence, our findings suggest that the ability to identify and control the best localized edge mode trumps any gains from introducing disorder.

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Section: Edge Mode Constructionmentioning

confidence: 99%

Edge mode locality in perturbed symmetry protected topological order

et al. 2019

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“…Knowledge of the local integrals of motion is equivalent to knowing the full many-body spectrum and, consequently, all physical properties of the system. However, despite a number of theoretical and numerical proposals, 16,[39][40][41][42][43][44] the explicit construction of LIOMS remains a partially open problem. Nevertheless, even partial knowledge about the statistical properties of LIOM can be useful.…”

Section: 25mentioning

confidence: 99%

Loschmidt echo in many-body localized phases

Serbyn¹,

Abanin²

2017

Phys. Rev. B

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The Loschmidt echo, defined as the overlap between quantum wave function evolved with different Hamiltonians, quantifies the sensitivity of quantum dynamics to perturbations and is often used as a probe of quantum chaos. In this work we consider the behavior of the Loschmidt echo in the many body localized phase, which is characterized by emergent local integrals of motion, and provides a generic example of non-ergodic dynamics. We demonstrate that the fluctuations of the Loschmidt echo decay as a power law in time in the many-body localized phase, in contrast to the exponential decay in few-body ergodic systems. We consider the spin-echo generalization of the Loschmidt echo, and argue that the corresponding correlation function saturates to a finite value in localized systems. Slow, power-law decay of fluctuations of such spin-echo-type overlap is related to the operator spreading and is present only in the many-body localized phase, but not in a non-interacting Anderson insulator. While most of the previously considered probes of dephasing dynamics could be understood by approximating physical spin operators with local integrals of motion, the Loschmidt echo and its generalizations crucially depend on the full expansion of the physical operators via local integrals of motion operators, as well as operators which flip local integrals of motion. Hence, these probes allow to get insights into the relation between physical operators and local integrals of motion, and access the operator spreading in the many-body localized phase.

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“…[34] in the regime where the system has good ergodic behavior. On the other hand, for large g, λ 0 (M) first decays exponentially with M but then turns into a slower decay at larger M. The exponential decay was also observed in the case of such "slowest operator" construction in the MBL phase [7]. This exponential behavior differentiates ) shows additional data from the Schrieffer-Wolff construction of quasiconserved quantity (see Sec.…”

Section: B Algorithmmentioning

confidence: 61%

“…In the MBL system, Ref. [7] used this approach to explicitly construct the approximately conserved operators as local integrals of motion. As we will show in the next Sec.…”

Section: B Relation To Operator Norm and Thermalization Time Scalementioning

confidence: 99%

Explicit construction of quasiconserved local operator of translationally invariant nonintegrable quantum spin chain in prethermalization

Lin

Motrunich

2017

Phys. Rev. B

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We numerically construct translationally invariant quasiconserved operators with maximum range M, which best commute with a nonintegrable quantum spin chain Hamiltonian, up to M = 12. In the large coupling limit, we find that the residual norm of the commutator of the quasiconserved operator decays exponentially with its maximum range M at small M, and turns into a slower decay at larger M. This quasiconserved operator can be understood as a dressed total "spin-z" operator, by comparing with the perturbative Schrieffer-Wolff construction developed to high order reaching essentially the same maximum range. We also examine the operator inverse participation ratio of the operator, which suggests its localization in the operator Hilbert space. The operator also shows an almost exponentially decaying profile at short distance, while the long-distance behavior is not clear due to limitations of our numerical calculation. Further dynamical simulation confirms that the prethermalization-equilibrated values are described by a generalized Gibbs ensemble that includes such quasiconserved operator.

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Explicit construction of local conserved operators in disordered many-body systems

Cited by 53 publications

References 40 publications

Edge mode locality in perturbed symmetry protected topological order

Edge mode locality in perturbed symmetry protected topological order

Loschmidt echo in many-body localized phases

Explicit construction of quasiconserved local operator of translationally invariant nonintegrable quantum spin chain in prethermalization

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