Probing the exchange statistics of one-dimensional anyon models

Greschner, Sebastian; Cardarelli, Lorenzo; Santos, Luís

doi:10.1103/physreva.97.053605

Cited by 18 publications

(13 citation statements)

References 63 publications

(85 reference statements)

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“…We conclude by discussing possible realizations of the model considered in this paper. Apart from theoretical ideas for realizing generalized statistics in one dimension [16][17][18][19][20] , systems of fermionic or bosonic atoms with density-dependent hoppings have been proposed theoretically [31][32][33][34][35][36][37][38][39] and realized experimentally 40,41 . The system studied in Ref.…”

Section: Discussionmentioning

confidence: 99%

“…Such generalizations can be introduced in many different ways, for instance, by modifying the conditions on the wave function and its derivative at the points when two of the particles have the same coordinate, modifying the commutation relations between the creation and annihilation operators in a second-quantized formalism, or modifying the form of the exclusion principle [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] . Several theoretical proposals have been made for realizing generalized statistics in one dimension [16][17][18][19][20] .…”

Section: Introductionmentioning

confidence: 99%

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Bosonization study of a generalized statistics model with four Fermi points

Aditya

Sen

2021

Phys. Rev. B

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We study a one-dimensional lattice model of fractional statistics in which particles have next-nearest-neighbor hopping between sites which depends on the occupation number at the intermediate site and a statistical parameter φ. The model breaks parity and time-reversal symmetries and has four-fermion interactions if φ = 0. We first analyze the model using mean field theory and find that there are four Fermi points whose locations depend on φ and the filling η. We then study the modes near the Fermi points using the technique of bosonization. Based on the quadratic terms in the bosonized Hamiltonian, we find that the low-energy modes form two decoupled Tomonaga-Luttinger liquids with different values of the Luttinger parameters which depend on φ and η; further, the right and left moving modes of each system have different velocities. A study of the scaling dimensions of the cosine terms in the Hamiltonian indicates that the terms appearing in one of the Tomonaga-Luttinger liquids will flow under the renormalization group and the system may reach a non-trivial fixed point in the long distance limit. We examine the scaling dimensions of various charge density and superconducting order parameters to find which of them is the most relevant for different values of φ and η. Finally we look at two-particle bound states that appear in this system and discuss their possible relevance to the properties of the system in the thermodynamic limit. Our work shows that the low-energy properties of this model of fractional statistics have a rich structure as a function of φ and η.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bosonization study of a generalized statistics model with four Fermi points

Aditya

Sen

2021

Phys. Rev. B

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“…The tails of the momentum distribution exhibit the universal 1/k 4 behavior with the amplitude given by Tan's contact which is a monotonic function of the statistics parameter. The natural extension of our work is the consideration of the equivalent lattice system, the 2AHM [87,88], in the strong repulsive limit. In the fermionic case, the well known Hubbard model, the determinant representation of the correlators is already known [139,140] and the long distance asymptotics of the static correlators has also been determined [141].…”

Section: Discussionmentioning

confidence: 99%

“…In this paper we investigate the correlation functions of a 1D two-component system with repulsive contact interactions which can be understood as the anyonic generalization of the Gaudin-Yang model. The literature on 1D anyonic models has been growing steadily in the last years spurred by several experimental proposals of realizing such systems with ultracold atoms in optical lattices using Raman-assisted tunneling [84,85], periodically driven lattices [86] or multicolor lattice-depth modulation [87,88]. Much of the attention was focused on single component systems like the anyonic Lieb-Liniger model [89][90][91] for which we know the ground state characterization [90,92], asymptotic behavior of the correlation functions for homogeneous [26,27,59,[93][94][95] and trapped systems [96,97], entanglement [98,99], and nonequilibrium [100][101][102] properties.…”

Section: Introductionmentioning

confidence: 99%

Correlation functions of one-dimensional strongly interacting two-component gases

Pâţu¹

2019

Phys. Rev. A

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We address the problem of calculating the correlation functions of one-dimensional two-component gases with strong repulsive contact interactions. The model considered in this paper describes particles with fractional statistics and in appropriate limits reduces to the Gaudin-Yang model or the spinor Bose gas. In the case of impenetrable particles we derive a Fredholm determinant representation for the temperature-, time-, and space-dependent correlation functions which is very easy to implement numerically and constitute the starting point for the analytical investigation of the asymptotics. Making use of this determinant representation and the solution of an associated Riemann-Hilbert problem we derive the low-energy asymptotics of the correlators in the spin-incoherent regime characterized by near ground-state charge degrees of freedom but a highly thermally disordered spin sector. The asymptotics present features reminiscent of spin-charge separation with the spin part exponentially decaying in space separation and oscillating with a period proportional to the statistics parameter while the charge part presents scaling with anomalous exponents which cannot be described by any unitary conformal field theory. The momentum distribution and the Fourier transform of the dynamical Green's function are asymmetrical for arbitrary statistics, a direct consequence of the broken space-reversal symmetry. Due to the exponential decay the momentum distribution n(k) at zero temperature does not present algebraic singularities but the tails obey the universal decay lim k→±∞ n(k) ∼ C/k 4 with the amplitude C given by Tan's contact. As a function of the statistics parameter the contact is a monotonic function reaching its minimum for the fermionic system and the maximum for the bosonic system.

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“…In this paper, we investigate the above issues in context of the paradigmatic Su-Schrieffer-Heeger (SSH) model for polyacetylene [10,11] that stabilises symmetry protected topological boundary modes. We examine an interesting tuning parameter that is of relevance in context of recent experimental [43,44] and theoretical [45][46][47] developments -the generalised algebra of the interacting fermions -and study it in context of two coupled SSH chains as shown in Fig. 1.…”

Section: Introductionmentioning

confidence: 99%

Statistics tuned entanglement of the boundary modes in coupled Su-Schrieffer-Heeger chains

Santra,

Agarwala,

Bhattacharjee

2020

Preprint

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We show that mutual statistics between quantum particles can be tuned to generate emergent novel few particle quantum mechanics for the boundary modes of symmetry-protected topological phases of matter. As a concrete setting, we study a system of pseudofermions, defined as quantum particles with tunable algebra, which lie on two distinct Su-Schrieffer-Heeger (SSH) chains. We find that as the mutual statistics of the particles are tuned -the boundary modes present in the two chains gets non-trivially entangled showing a sudden jump in their mutual entanglement entropy. We further show that, such tuning of statistics engenders a first-order transition between two topologically non-trivial phases which differ in the behavior of inter-chain entanglement. Using a combination of analytical and numerical techniques and effective modeling, we uncover the rich physics that this system hosts. The results are of particular relevance in context of the study of the effective low energy quantum mechanics of topological edge modes in one hand and their recent realization in ultracold atoms on the other. This then provides for controlled manipulation of such low energy modes.

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Probing the exchange statistics of one-dimensional anyon models

Cited by 18 publications

References 63 publications

Bosonization study of a generalized statistics model with four Fermi points

Bosonization study of a generalized statistics model with four Fermi points

Correlation functions of one-dimensional strongly interacting two-component gases

Statistics tuned entanglement of the boundary modes in coupled Su-Schrieffer-Heeger chains

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