Dissipative spin chains: Implementation with cold atoms and steady-state properties

We study relaxation times, also called mixing times, of quantum many-body systems described by a Lindblad master equation. We in particular study the scaling of the spectral gap with the system length, the so-called dynamical exponent, identifying a number of transitions in the scaling. For systems with bulk dissipation we generically observe different scaling for small and for strong dissipation strength, with a critical transition strength going to zero in the thermodynamic limit. We also study a related phase transition in the largest decay mode. For systems with only boundary dissipation we show a generic bound that the gap can not be larger than ∼ 1/L. In integrable systems with boundary dissipation one typically observes scaling ∼ 1/L 3 , while in chaotic ones one can have faster relaxation with the gap scaling as ∼ 1/L and thus saturating the generic bound. We also observe transition from exponential to algebraic gap in systems with localized modes.

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“…Refs. [31,32], with individual components like few qubit controlled dissipation [33] or Heisenberg spin chains [34,35] already demonstrated.…”

Section: Lindblad Equationmentioning

confidence: 99%

Relaxation times of dissipative many-body quantum systems

2015

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“…cos(θ bb )( S i · S i+1 ) + sin(θ bb )( S i · S i+1 ) 2 (8) can be expressed in terms of the projectors P (1) i and P (2) i as follows,…”

Section: The Anyonic Quantum Spin Chain Hamiltoniansmentioning

confidence: 99%

“…Over the years, a plethora of physical systems that connect to the elementary physics of quantum spin chains have been identified, including transition metal oxides 6 , Au quantum wires on semiconducting surfaces 7 , or ultra-cold atoms in optical lattices 8 . Recently, it has been realized that certain 'deformations' of quantum spins can be used to describe some of the more peculiar topological properties of exotic quasiparticles, so-called non-Abelian anyons, that arise in certain topologically ordered systems, including certain fractional quantum Hall states 9 , p x + ip y superconductors 10 , heterostructures of topological insulators and superconductors 11 , heterostructures of spin-orbit coupled semiconductors and superconductors 12 and possibly certain Iridates 13 which may effectively realize the Kitaev honeycomb model 14 .…”

Section: Introductionmentioning

confidence: 99%

Anyonic quantum spin chains: Spin-1 generalizations and topological stability

et al. 2013

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There are many interesting parallels between systems of interacting non-Abelian anyons and quantum magnetism, occuring in ordinary SU(2) quantum magnets. Here we consider theories of so-called su(2) k anyons, well-known deformations of SU (2), in which only the first k + 1 angular momenta of SU(2) occur. In this manuscript, we discuss in particular anyonic generalizations of ordinary SU(2) spin chains with an emphasis on anyonic spin S = 1 chains. We find that the overall phase diagrams for these anyonic spin-1 chains closely mirror the phase diagram of the ordinary bilinear-biquadratic spin-1 chain including anyonic generalizations of the Haldane phase, the AKLT construction, and supersymmetric quantum critical points. A novel feature of the anyonic spin-1 chains is an additional topological symmetry that protects the gapless phases. Distinctions further arise in the form of an even/odd effect in the deformation parameter k when considering su(2) k anyonic theories with k ≥ 5, as well as for the special case of the su(2)4 theory for which the spin-1 representation plays a special role. We also address anyonic generalizations of spin-1/2 chains with a focus on the topological protection provided for their gapless ground states. Finally, we put our results into context of earlier generalizations of SU(2) quantum spin chains, in particular so-called (fused) Temperley-Lieb chains.

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“…It is well known that spin chains can exhibit kinds of quantum disorder and of quantum chaos [8,9,10,11], and that quantum synchronization is related to the entanglement [12,13,14,15]. To involve a kind of chimera states, our model consists of a non-hermitian spin chain [16,17,19,22] which can be assimilated to a spin chain in contact with an environment. This model is presented next section.…”

Section: Introductionmentioning

confidence: 99%

Quantum chimera states

Viennot

Aubourg

2016

Physics Letters A

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We study a theoretical model of closed quasi-hermitian chain of spins which exhibits quantum analogues of chimera states, i.e. long life classical states for which a part of an oscillator chain presents an ordered dynamics whereas another part presents a disordered dynamics. For the quantum analogue, the chimera behavior deals with the entanglement between the spins of the chain. We discuss the entanglement properties, quantum chaos, quantum disorder and semiclassical similarity of our quantum chimera system. The quantum chimera concept is novel and induces new perspectives concerning the entanglement of multipartite systems.

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Dissipative spin chains: Implementation with cold atoms and steady-state properties

Cited by 30 publications

References 33 publications

Relaxation times of dissipative many-body quantum systems

Relaxation times of dissipative many-body quantum systems

Anyonic quantum spin chains: Spin-1 generalizations and topological stability

Quantum chimera states

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