A rescaling approach to two- and three-dimensional lattice spectra

Southern, B. W.; Loly, P. D.

doi:10.1088/0305-4470/18/3/026

Cited by 8 publications

(5 citation statements)

References 21 publications

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“…( 13) and insert its value in the remaining equations. Notice that different decimation strategies might be more favorable, depending on the Green's function of interest and/or the geometry of the system [40][41][42][43]45,48,50]. After decimating site 1, we find that the equations of motion can be written as…”

Section: A Real-space Decimation: Methodsmentioning

confidence: 99%

“…In what follows, we show how to use decimation [27,28] to obtain the lattice Green's functions, G j,l (ω), in both models. This technique has been successfully applied in the Hermitian scenario [40][41][42][43]45,48,50] mainly to determine the surface Green's function. However, as we will show now, since these results are based on a self-similarity transformation, they can be directly extrapolated to the dissipative scenario and can be used to characterize arbitrary Green's functions.…”

Section: Decimation For Lattice Green's Functionsmentioning

confidence: 99%

“…However, they have also been recently pointed out as a useful tool to characterize out-of-equilibrium situations subject to time-dependent drives [35,36] and/or coupling to environments, in combination with the Keldysh formalism [37][38][39]. Decimation techniques [27,28] have already been applied to calculate lattice Green's functions in closed-system scenarios in one- [40][41][42][43][44] and higherdimensional lattices [45][46][47], including some topological models [48][49][50]. Here, we show how to apply this technique FIG.…”

Section: Introductionmentioning

confidence: 99%

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Decimation technique for open quantum systems: A case study with driven-dissipative bosonic chains

et al. 2022

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The unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (nonunitary) dynamics, which can be radically different from closed-system scenarios. Such open quantum system dynamics is generally described by Lindblad master equations, whose dynamical and steady-state properties are challenging to obtain, especially in the many-particle regime. Here, we introduce a method to deal with these systems based on the calculation of a (dissipative) lattice Green's function with a real-space decimation technique. Compared to other methods, such a technique enables us to obtain compact analytical expressions for the dynamics and steady-state properties, such as asymptotic decays or correlation lengths. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity, including the Hatano-Nelson model. The latter is especially illustrative because its surface and bulk dissipative behavior are linked due to its nontrivial topology, which manifests in directional amplification.

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Section: A Real-space Decimation: Methodsmentioning

confidence: 99%

Section: Decimation For Lattice Green's Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Decimation technique for open quantum systems: A case study with driven-dissipative bosonic chains

et al. 2022

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“…The reduction of a parent two-ring geometry into a two-site system can be done with the help of traditional real space renormaliztion group (RSRG) approach [58][59][60][61][62]. Below we describe this prescription brie y.…”

Section: Appendix B Renormalization Procedure: Step-by-step Derivatio...mentioning

confidence: 99%

Manipulation of circular currents in a coupled ring system: effects of connectivity and non-uniform disorder

Majhi¹,

Maiti²

2020

J. Phys.: Condens. Matter

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Considering a quantum network, here we propose two kinds of circular charge currents. These are referred as: net current in the full system and the current con ned within a particular segment of the network. The network is composed of two rings, where one of the rings is subjected to a magnetic ux. Depending on the connectivity among the rings a new kind of states, insensitive to the magnetic ux, is generated along with the current carrying states. Because of this, a pronounced oscillation in net current with lling factor appears which suggests a possible switching action. Appearance of these vanishing current carrying states gradually decreases with increasing the degree of connectivity between the rings. As long as the rings are coupled by using more than a single bond, a circular current of other kind appears in the ux free ring which induces a strong magnetic eld. The strength of this induced magnetic eld can be regulated selectively by tuning the magnetic ux in the other ring. This phenomenon can be utilized for spin switching and other spintronic applications. Finally, we examine the role of non-uniform disorder on these currents, and nd several atypical signatures. Our study can be generalized to any higher loop system for investigating magneto-transport properties.

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“…However, they have also been recently pointed out as a useful tool to characterize out-of-equilibrium situations subject to time-dependent drives [35,36] and/or coupling to environments, in combination with Keldysh formalism [37][38][39]. Decimation techniques [27,28] have already been applied to calculate lattice Green's functions in closed-system scenarios in one [40][41][42][43] and higher-dimensional lattices [44][45][46], including some topological models [47][48][49]. Here, we show how to apply this technique in generic open quantum systems, where it has been scarcely used [50].…”

Section: Introductionmentioning

confidence: 99%

Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains

Gómez-León,

Ramos,

Porras

et al. 2022

Preprint

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A rescaling approach to two- and three-dimensional lattice spectra

Cited by 8 publications

References 21 publications

Decimation technique for open quantum systems: A case study with driven-dissipative bosonic chains

Decimation technique for open quantum systems: A case study with driven-dissipative bosonic chains

Manipulation of circular currents in a coupled ring system: effects of connectivity and non-uniform disorder

Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains

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