Dynamical symmetry approach to path integrals of quantum spin systems

Ringel, Matouš; Gritsev, Vladimir

doi:10.1103/physreva.88.062105

Cited by 27 publications

(137 citation statements)

References 51 publications

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“…The first class is formed by the models whose Hamiltonians are linear combinations of the generators of (in principle) arbitrary Lie algebras. For this class of Hamiltonians there is no distinction between quantum and classical dynamics, both of which map to a closed system of linear dif-ferential equations [30][31][32][33][34]. These generators can be always represented by the linear and bilinear forms of the creation-annihilation operators, for example using the bosons or fermions (see the second part of the book [30] and Ref.…”

Section: Floquet Theory: Setupmentioning

confidence: 99%

Integrable Floquet dynamics

2017

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We discuss several classes of integrable Floquet systems, i.e. systems which do not exhibit chaotic behavior even under a time dependent perturbation. The first class is associated with finite-dimensional Lie groups and infinite-dimensional generalization thereof. The second class is related to the row transfer matrices of the 2D statistical mechanics models. The third class of models, called here "boost models", is constructed as a periodic interchange of two Hamiltonians -one is the integrable lattice model Hamiltonian, while the second is the boost operator. The latter for known cases coincides with the entanglement Hamiltonian and is closely related to the corner transfer matrix of the corresponding 2D statistical models. We present several explicit examples. As an interesting application of the boost models we discuss a possibility of generating periodically oscillating states with the period different from that of the driving field. In particular, one can realize an oscillating state by performing a static quench to a boost operator. We term this state a "Quantum Boost Clock". All analyzed setups can be readily realized experimentally, for example in cold atoms.

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Section: Floquet Theory: Setupmentioning

confidence: 99%

Integrable Floquet dynamics

2017

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“…As noted in [21] except for V 0 all higher order V n are identically equal to zero for linear dispersion and this can easily be derived by partial fraction expansion of the integrands in V n and the simpler form of H(z; k) in the case of linear dispersion where I(z) actually becomes independent of z. The same result can also be obtained via a path integral approach [64]. Also note that, the infinite series we obtain for the free to free scattering channel in the two photon case agrees with the results of the previous section, compare (41), (42), (43), (44) and (45) with (40).…”

Section: Perturbative Analysis Of Free To Free Scatteringmentioning

confidence: 67%

Effects of modal dispersion on few-photon–qubit scattering in one-dimensional waveguides

Kocabaş

2016

Phys. Rev. A

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We study one-and two-photon scattering from a qubit embedded in a one-dimensional waveguide in the presence of modal dispersion. We use a resolvent based analysis and utilize techniques borrowed from the Lee model studies. Modal dispersion leads to atom-photon bound states which necessitate the use of multichannel scattering theory. We present multichannel scattering matrix elements in terms of the solution of a Fredholm integral equation of the second kind. Through the use of the Lippmann-Schwinger equation, we derive an infinite series of Feynman diagrams that represent the solution to the integral equation. We use the Feynman diagrams as vertex correction terms to come up with closed form formulas that successfully predict the trapping rate of a photon in the atom-photon bound state. We verify our formalism through Krylov-subspace based numerical studies with pulsed excitations. Our results provide the tools to calculate the complex correlations between scattered photons in a dispersive environment.

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“…In many-body quantum models, SDEs are used in the investigation of nonequilibrium quantum dynamical phenomena in the form of the effective EoM of the collective quantum modes [20] and order parameters [21]. They also represent a useful tool for quantum statistics [22]. In other scientific disciplines, SDEs are even more fundamental, as they appear at the level of the very formulation of dynamics, unlike the EoM in physics, which descend from least action principles.…”

Section: A Dynamical Long-range Ordermentioning

confidence: 99%

Introduction to Supersymmetric Theory of Stochastics

Овчинников

2016

Entropy

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Many natural and engineered dynamical systems, including all living objects, exhibit signatures of what can be called spontaneous dynamical long-range order (DLRO). This order's omnipresence has long been recognized by the scientific community, as evidenced by a myriad of related concepts, theoretical and phenomenological frameworks, and experimental phenomena such as turbulence, $1/f$ noise, dynamical complexity, chaos and the butterfly effect, the Richter scale for earthquakes and the scale-free statistics of other sudden processes, self-organization and pattern formation, self-organized criticality, etc. Although several successful approaches to various realizations of DLRO have been established, the universal theoretical understanding of this phenomenon remained elusive. The possibility of constructing a unified theory of DLRO has emerged recently within the approximation-free supersymmetric theory of stochastics (STS). There, DLRO is the spontaneous breakdown of the topological or de Rahm supersymmetry that all stochastic differential equations (SDEs) possess. This theory may be interesting to researchers with very different backgrounds because the ubiquitous DLRO is a truly interdisciplinary entity. The STS is also an interdisciplinary construction. This theory is based on dynamical systems theory, cohomological field theories, the theory of pseudo-Hermitian operators, and the conventional theory of SDEs. Reviewing the literature on all these mathematical disciplines can be time consuming. As such, a concise and self-contained introduction to the STS, the goal of this paper, may be useful.Comment: 98 pages; 13 figures; revtex 4-

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Dynamical symmetry approach to path integrals of quantum spin systems

Cited by 27 publications

References 51 publications

Integrable Floquet dynamics

Integrable Floquet dynamics

Effects of modal dispersion on few-photon–qubit scattering in one-dimensional waveguides

Introduction to Supersymmetric Theory of Stochastics

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