Fulde-Ferrell-Larkin-Ovchinnikov states in a superconducting ring with magnetic fields: Phase diagram and the first-order phase transitions

Yoshii, Ryosuke; Takada, Satoshi; Tsuchiya, Shunji; Marmorini, Giacomo; Hayakawa, Hisao; Nitta, Muneto

doi:10.1103/physrevb.92.224512

Cited by 25 publications

(27 citation statements)

References 33 publications

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“…More generally, multiple twisted kinks with arbitrary phase and positions [75,76] can be further constructed systematically due to the integrable structure behind the model known as the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy for the nonlinear Schrödinger equation [77][78][79]. Recent developments include time-dependent soliton scatterings [80,81], multi-component condensates [82][83][84], a ring geometry [85], and an interval with a Casimir force [86].…”

Section: Jhep12(2017)145mentioning

confidence: 99%

Self-consistent large-N analytical solutions of inhomogeneous condensates in quantum ℂPN − 1 model

Nitta

Yoshii

2017

J. High Energ. Phys.

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We give, for the first time, self-consistent large-N analytical solutions of inhomogeneous condensates in the quantum CP N −1 model in the large-N limit. We find a map from a set of gap equations of the CP N −1 model to those of the Gross-Neveu (GN) model (or the gap equation and the Bogoliubov-de Gennes equation), which enables us to find the self-consistent solutions. We find that the Higgs field of the CP N −1 model is given as a zero mode of solutions of the GN model, and consequently only topologically nontrivial solutions of the GN model yield nontrivial solutions of the CP N −1 model. A stable single soliton is constructed from an anti-kink of the GN model and has a broken (Higgs) phase inside its core, in which CP N −1 modes are localized, with a symmetric (confining) phase outside. We further find a stable periodic soliton lattice constructed from a real kink crystal in the GN model, while the Ablowitz-Kaup-Newell-Segur hierarchy yields multiple solitons at arbitrary separations.

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Section: Jhep12(2017)145mentioning

confidence: 99%

Self-consistent large-N analytical solutions of inhomogeneous condensates in quantum ℂPN − 1 model

Nitta

Yoshii

2017

J. High Energ. Phys.

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“…For example, Bruno [7] and Nozières [8] discussed some difficulties in realizing time crystals. However, since their arguments were not fully general, several new realizations of time crystals, which avoid these no-go arguments, were proposed [9,10].In fact, a part of the confusion can be attributed to the lack of a precise mathematical definition of time crystals. Here, we first propose a definition of time crystals in the equilibrium, which is a natural generalization of that of ordinary crystals and can be formulated precisely also for time crystals.…”

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Absence of Quantum Time Crystals

2015

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In analogy with crystalline solids around us, Wilczek recently proposed the idea of "time crystals" as phases that spontaneously break the continuous time translation into a discrete subgroup. The proposal stimulated further studies and vigorous debates whether it can be realized in a physical system. However, a precise definition of the time crystal is needed to resolve the issue. Here we first present a definition of time crystals based on the time-dependent correlation functions of the order parameter. We then prove a no-go theorem that rules out the possibility of time crystals defined as such, in the ground state or in the canonical ensemble of a general Hamiltonian, which consists of not-too-long-range interactions.Recently, Wilczek proposed a fascinating new concept of time crystals, which spontaneously break the continuous time translation symmetry, in analogy with ordinary crystals which break the continuous spatial translation symmetry [1][2][3]. Li et al. soon followed with a concrete proposal for an experimental realization and observation of a (space-)time crystal, using trapped ions in a ring threaded by an Aharonov-Bohm flux [4][5][6]. While the proposal of time crystals was quite bold, it is, on the other hand, rather natural from the viewpoint of relativity: since we live in the Lorentz invariant space-time, why don't we have time crystals if there are ordinary crystals with a long-range order in spatial directions?However, the very existence, even as a matter of principle, of time crystals is rather controversial. For example, Bruno [7] and Nozières [8] discussed some difficulties in realizing time crystals. However, since their arguments were not fully general, several new realizations of time crystals, which avoid these no-go arguments, were proposed [9,10].In fact, a part of the confusion can be attributed to the lack of a precise mathematical definition of time crystals. Here, we first propose a definition of time crystals in the equilibrium, which is a natural generalization of that of ordinary crystals and can be formulated precisely also for time crystals. We then prove generally the absence of time crystals defined as such, in the equilibrium with respect to an arbitrary Hamiltonian which consists of not-too-long-range interactions. We present two theorems: one applies only to the ground state, and the other applies to the equilibrium with an arbitrary temperature.Naively, time crystals would be defined in terms of the expectation value Ô (t) of an observableÔ(t). If Ô (t) exhibits a periodic time dependence, the system may be regarded as a time crystal. However, the very definition of eigenstatesĤ|n = E n |n immediately implies that the expectation value of any Heisenberg operatorÔ(t) ≡ e iĤtÔ (0)e −iĤt in the Gibbs equilibrium ensemble is time independent. To see this, recall that the expectation value X is defined as X ≡ 0|X|0 at zero temperature T = 0 and X ≡ tr(Xe −βĤ )/Z = n n|X|n e −βEn /Z at a finite temperature T = β −1 > 0, where |0 is the ground state and Z ≡ tr[e −βĤ ] is th...

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“…1. Two different systems have been proposed: a bright soliton formed by attractively interacting particles on an Aharonov-Bohm ring [6] and ions on a ring in the presence of an external magnetic field [7] (see also [8][9][10][11][12]). These proposals triggered debate in the literature whether time crystal formation is possible.…”

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Modeling spontaneous breaking of time-translation symmetry

2015

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We show that an ultra-cold atomic cloud bouncing on an oscillating mirror can reveal spontaneous breaking of a discrete time translation symmetry. In many-body simulations we illustrate the process of the symmetry breaking that can be induced by atomic losses or by a measurement of particle positions. The results pave the way for understanding and realization of the time crystal idea where crystalline structures form in the time domain due to spontaneous breaking of continuous time translation symmetry. 03.75.Lm, Symmetries of a quantum many-body Hamiltonian are reflected by properties of its eigenstates. However, there are systems whose eigenstates are extremely vulnerable to any symmetry breaking perturbation. Bose gas in a symmetric double well potential, with attractive particle interactions, is a simple example [1][2][3][4][5]. The ground state of the system reflects the symmetry of the external potential but it cannot be easily prepared in an experiment because it is a macroscopic superposition of two Bose-Einstein condensates (BEC) located in different potential wells. Loss of a particle is sufficient to break the symmetry and accumulate all remaining particles in one of the wells. Breaking of a symmetry due to an infinitesimally weak perturbation is called spontaneous symmetry breaking phenomenon.Spontaneous breaking of continuous spatial translation symmetry to discrete spatial translation symmetry is responsible for formation of space crystals. Recently it has been proposed that similar phenomenon can also occur in the time domain [6,7]. That is, it is possible to invent systems where the ground state of a time-independent Hamiltonian reveals spatially homogeneous flow of particles which under any symmetry breaking perturbation changes spontaneously to periodic motion of spatially inhomogeneous structures. Such a spontaneous breaking of continuous time translation symmetry to a discrete one is termed time crystal formation, see Fig. 1. Two different systems have been proposed: a bright soliton formed by attractively interacting particles on an Aharonov-Bohm ring [6] and ions on a ring in the presence of an external magnetic field [7] (see also [8][9][10][11][12]). These proposals triggered debate in the literature whether time crystal formation is possible. It seems that different assumptions can lead to contradictory conclusions [13][14][15][16][17][18][19][20][21][22].In the present paper we consider a periodically driven many-body system whose description can be reduced to a Hilbert space spanned by two periodically evolving modes. As in the case of a Bose gas in a double well potential [1-5], a spontaneous symmetry breaking process occurs. In our example, eigenstates of the system pos- sess discrete time translation symmetry which is spontaneously broken to another discrete translation symmetry but with a longer period, see Fig. 1. The spontaneous symmetry breaking that is predicted within the mean field approach, can be analyzed in full many-body simulations. Moreover it can be realized in ultra-...

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Fulde-Ferrell-Larkin-Ovchinnikov states in a superconducting ring with magnetic fields: Phase diagram and the first-order phase transitions

Cited by 25 publications

References 33 publications

Self-consistent large-N analytical solutions of inhomogeneous condensates in quantum ℂPN − 1 model

Self-consistent large-N analytical solutions of inhomogeneous condensates in quantum ℂPN − 1 model

Absence of Quantum Time Crystals

Modeling spontaneous breaking of time-translation symmetry

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