Berry’s phases of ground states of interacting spin-one bosons: Chains of monopoles and monosegments

Wiemer, J.D.W.; Zhou, Fei

doi:10.1103/physrevb.70.115110

Cited by 5 publications

(3 citation statements)

References 38 publications

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“…Possible applications range from optics and molecular physics to fundamental quantum mechanics and quantum computation [3]. In condensed matter physics a variety of phenomena have been understood as a manifestation of topological or geometric phases [4,5,6,7,8]. An interesting open question is whether the geometric phases can be used to investigate the physics and the behavior of condensed matter systems.…”

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confidence: 99%

Geometric Phases and Criticality in Spin-Chain Systems

2005

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A relation between geometric phases and criticality of spin chains is established. As a result, we show how geometric phases can be exploited as a tool to detect regions of criticality without having to undergo a quantum phase transition. We analytically evaluate the geometric phase that correspond to the ground and excited states of the anisotropic XY model in the presence of a transverse magnetic field when the direction of the anisotropy is adiabatically rotated. It is demonstrated that the resulting phase is resilient against the main sources of errors. A physical realization with ultra-cold atoms in optical lattices is presented.PACS numbers: 03.65. Vf, 05.30.Pr, 42.50.Vk Since the discovery by Berry [1], geometric phases in quantum mechanics have been the subject of a variety of theoretical and experimental investigations [2]. Possible applications range from optics and molecular physics to fundamental quantum mechanics and quantum computation [3]. In condensed matter physics a variety of phenomena have been understood as a manifestation of topological or geometric phases [4,5,6,7,8]. An interesting open question is whether the geometric phases can be used to investigate the physics and the behavior of condensed matter systems. Here we show how to exploit the geometric phase as an essential tool to reveal quantum critical phenomena in many-body quantum systems. Indeed, quantum phase transitions are accompanied by a qualitative change in the nature of classical correlations and their description is clearly one of the major interests in condensed matter physics [9,10]. Such drastic changes in the properties of ground states are often due to the presence of points of degeneracy and are reflected in the geometry of the Hilbert space of the system. The geometric phase, which is a measure of the curvature of the Hilbert space, is able to capture them, thereby revealing critical behavior. This provides the means to detect, not only theoretically, but also experimentally the presence of criticality without having to undergo a quantum phase transition.In this letter we analyze the XY spin chain model and the geometric phase that corresponds to the XX criticality. Since the XY model is exactly solvable and still presents a rich structure it offers a benchmark to test the properties of geometric phases in the proximity of a quantum phase transition. Indeed, we observe that, an excitation of the model obtains a non-trivial Berry phase if and only if it circulates a region of criticality. The generation of this phase can be traced down to the presence of a conical intersection of the energy levels located at the XX criticality. This geometric interpretation reveals a relation between the critical exponents of the model. The insights provided here shed light into the understanding of more general systems, where analytic solutions might not be available. A physical implementation is proposed with ultra-cold atoms superposed by optical lattices [11,12]. It utilizes Raman activated tunneling transitions as well as coher...

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Geometric Phases and Criticality in Spin-Chain Systems

2005

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“…So far there have been two theoretical approaches to studying the Berry phase in many-body systems: the fully quantummechanical treatment and the mean-field treatment. In the full quantum description, the Berry phases and criticality in a spin-chain system [18], dynamics and the Berry phase of two-species Bose-Einstein condensates (BECs) [19], and the Berry phases of ground states of interacting spin-1 bosons [20] have been reported. In this description, the Berry phase for finite interacting particles can still be expressed as the circuit integral of the Berry connection of the many-body instantaneous eigenstate.…”

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confidence: 99%

Berry phase and Hannay angle of an interacting boson system

Liu

2011

Phys. Rev. A

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In the present paper, we investigate the Berry phase and the Hannay angle of an interacting two-mode boson system and obtain their analytic expressions in explicit forms. The relation between the Berry phase and the Hannay angle is discussed. We find that, in the large-particle-number limit, the classical Hannay angle equals the particle number derivative of the quantum Berry phase except for a sign. This relationship is applicable to other many-body boson systems where the coherent-state description is available and the total particle number is conserved. The measurement of the classical Hannay angle in the many-body systems is briefly discussed as well.

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“…Staircase in an anti-ferromagnetic spin-1 BEC. We consider a spin-1 anti-ferromagnetic BEC with an applied field p in the z-direction leading to the Hamiltonian H = cS 2 − pS z , where c > 0 [30,31]. For sufficiently small magnetic field, we can omit the quadratic Zeeman terms.…”

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Staircase in magnetization and entanglement entropy of spinor condensates

2018

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Staircases in response functions are associated with physically observable quantities that respond discretely to continuous tuning of a control parameter. A well-known example is the quantization of the Hall conductivity in two dimensional electron gases at high magnetic fields. Here, we show that such a staircase response also appears in the magnetization of spin-1 atomic ensembles evolving under several spin-squeezing Hamiltonians. We discuss three examples, two mesoscopic and one macroscopic, where the system's magnetization vector responds discretely to continuous tuning of the applied magnetic field or the atom density, thus producing a magnetization staircase. The examples that we consider are directly related to Hamiltonians that have been implemented experimentally in the context of spin and spin-nematic squeezing. Thus, our results can be readily put to experimental test in spin-1 ferromagnetic 87 Rb and anti-ferromagnetic 23 Na condensates. arXiv:1804.03745v1 [cond-mat.quant-gas]

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Berry’s phases of ground states of interacting spin-one bosons: Chains of monopoles and monosegments

Cited by 5 publications

References 38 publications

Geometric Phases and Criticality in Spin-Chain Systems

Geometric Phases and Criticality in Spin-Chain Systems

Berry phase and Hannay angle of an interacting boson system

Staircase in magnetization and entanglement entropy of spinor condensates

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