Integrable supersymmetric chain without particle conservation

Gier, Jan de; Fehér, G.; Nienhuis, Bernard; Rusaczonek, Magdalena

doi:10.1088/1742-5468/2016/02/023104

Cited by 7 publications

(17 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section, we define the models [1,2]. We refer to the model of [1] as FS model, and the model of [2] as FGNR model. Both are spinless fermion models on a chain of length L with some boundary conditions.…”

Section: Modelsmentioning

confidence: 99%

“…Originally, the FS model was considered with open boundary conditions [1] and the FGNR model with periodic boundary conditions [2]. In this section we give a short overview of [1] and [2]. In Section 3 we restrict ourselves to the open boundary conditions for both models with even L and discuss the mapping between them.…”

Section: Modelsmentioning

confidence: 99%

“…The second model we discuss was introduced by Feher, de Gier, Nienhuis and Ruzaczonek (FGNR) [2]. It can be viewed as a particle-hole symmetric version of the M 1 model, where the 'exclusion' constraint on the Hilbert space has been relaxed and where the supercharges are now symmetric between particles and holes.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Curious Mapping Between Supersymmetric Quantum Chains

et al. 2019

View full text Add to dashboard Cite

We present a unitary transformation relating two apparently different supersymmetric lattice models in one dimension. The first [1] describes semionic particles on a 1D ladder, with supersymmetry moving particles between the two legs. The second [2] is a fermionic model with particle-hole symmetry and with supersymmetry creating or annihilating pairs of domain walls. The mapping we display features non-trivial phase factors that generalise the sign factors occurring in the Jordan-Wigner transformation.We dedicate this work to our friend and colleague Bernard Nienhuis, on the occasion of his 65-th birthday.

show abstract

Section: Modelsmentioning

confidence: 99%

Section: Modelsmentioning

confidence: 99%

See 1 more Smart Citation

A Curious Mapping Between Supersymmetric Quantum Chains

et al. 2019

View full text Add to dashboard Cite

show abstract

“…Many-body supersymmetry preserving zero-energy ground states can be constructed as eigenstates of many-body Hamiltonians by considering supersymmetry in the non-relativistic setting, as in statistical physics, see [33,34] and citations therein. Supersymmetric many-body systems have been considered in the past [35], where their lattice formulation was done by realizing the global supercharges on the total Hilbert space of the system [36][37][38][39][40][41]. Exact solutions for these models were obtained in [42].…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric many-body systems from partial symmetries — integrability, localization and scrambling

Padmanabhan

Rey

Teixeira

et al. 2017

J. High Energ. Phys.

View full text Add to dashboard Cite

Partial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to realize supersymmetry in (0+1) dimensions and to build many-body quantum systems on a chain. This construction consists in associating appropriate supercharges to chain sites, in analogy to what is done in spin chains. For simple enough choices of supercharges, we show that the resulting states have a finite non-zero Witten index, which is invariant under perturbations, therefore defining supersymmetric phases of matter protected by the index. The Hamiltonians we obtain are integrable and display a spectrum containing both product and entangled states. By introducing disorder and studying the out-of-time-ordered correlators (OTOC), we find that these systems are in the many-body localized phase and do not thermalize. Finally, we reformulate a theorem relating the growth of the second Rényi entropy to the OTOC on a thermal state in terms of partial symmetries.

show abstract

“…Many-body supersymmetry preserving zero-energy ground states can be constructed as eigenstates of many-body hamiltonians by considering supersymmetry in the nonrelativistic setting, as in statistical physics, see [198,199] and citations therein. Supersymmetric manybody systems have been considered in the past [200], where their lattice formulation was done by realizing the global supercharges on the total Hilbert space of the system [201,202,203,204,205,206].…”

Section: Introductionmentioning

confidence: 99%

Aspects of entanglement, chaos and complexity: from many-body to high energy systems

Júnior¹

View full text Add to dashboard Cite

The determination of structures that can emerge out of the interactions among the constituents of a quantum many-body system is a foundational task of condensed matter physics. One of the most advanced proposals within this paradigm is the holographic generation of spacetime in some strongly coupled chaotic systems with particular patterns of entanglement and quantum complexity, which is historically motivated by the holographic principle and by the AdS/CFT correspondence. As a part of this scenario, this thesis is dedicated to the analysis of some concepts that are relevant to such proposal, where they are separately applied to some lattice models. Concretely, the matter is divided into three main studies: first, the calculation of the time-dependent circuit complexity in the Ising model with a periodically driven transverse field, where we establish the effectiveness of this quantity for the detection of nonequilibrium quantum phase transitions. Our results provide hints for understanding how universal features out of equilibrium are captured by the complexity of quantum states. Second, the derivation of a bound on the maximal rate of entanglement entropy production for a class of one-dimensional quantum circuits with periodic dynamics. An example of a circuit that saturates the bound is composed by parallel SWAP gates acting on entangled pairs. Out of inequalities obeyed by the entropy, in addition to considerations on multipartite entanglement, we indicate that the effect of a chaotic dynamics cannot result in the increase on the rate of entanglement production. Third, the construction of a class of supersymmetric many-body systems using symmetric inverse semigroups. For particular toy models built out of this structure, we study some questions regarding supersymmetric phases, integrability, disorder, spreading of quantum information and many-body localization. Finally, besides those three works, we include an essay addressing the problem of emergent holographic spaces out of two-dimensional conformal field theories, where the mediation between the two parts is performed by means of a Riemannian structure defined in the Hilbert space of the field theory.

show abstract

Integrable supersymmetric chain without particle conservation

Cited by 7 publications

References 12 publications

A Curious Mapping Between Supersymmetric Quantum Chains

A Curious Mapping Between Supersymmetric Quantum Chains

Supersymmetric many-body systems from partial symmetries — integrability, localization and scrambling

Aspects of entanglement, chaos and complexity: from many-body to high energy systems

Contact Info

Product

Resources

About