Exact Results for a Quantum Many-Body Problem in One Dimension

Sutherland, Bill

doi:10.1103/physreva.4.2019

Cited by 827 publications

(618 citation statements)

References 15 publications

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“…Recent studies have revealed that exactly solvable and integrable one-dimensional quantum many body systems with long-range interactions [1][2][3][4][5][6][7][8] are closely connected with a wide range of topics in modern physics as well as mathematics. In particular, this type of exactly solv-able systems have appeared as prototype models of various condensed matter systems exhibiting generalized exclusion statistics [8][9][10], quantum Hall effect [11] and quantum electric transport phenomena [12,13].…”

Section: Introductionmentioning

confidence: 99%

The spin Sutherland model of type and its associated spin chain

2011

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In this paper we study the su(m) spin Sutherland (trigonometric) model of D N type and its related spin chain of Haldane-Shastry type obtained by means of Polychronakos's freezing trick. As in the rational case recently studied by the authors, we show that these are new models, whose properties cannot be simply deduced from those of their well-known BC N counterparts by taking a suitable limit. We identify the Weyl-invariant extended configuration space of the spin dynamical model, which turns out to be the N-dimensional generalization of a rhombic dodecahedron. This is in fact one of the reasons underlying the greater complexity of the models studied in this paper in comparison with both their rational and BC N counterparts. By constructing a non-orthogonal basis of the Hilbert space of the spin dynamical model on which its Hamiltonian acts triangularly, we compute its spectrum in closed form. Using this result and applying the freezing trick, we derive an exact expression for the partition function of the associated Haldane-Shastry spin chain of D N type.

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Section: Introductionmentioning

confidence: 99%

The spin Sutherland model of type and its associated spin chain

2011

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“…Unfortunately, the exact density matrix for this model can be obtained only for a few special values of λ [2,12], so the question of the nature of crossover from the free fermion to the interacting non-Fermi liquid state can not be addressed exactly in this model. In the present work, we consider a one-dimensional wave function of the above form which can be considered as a generalization of the wavefunction corresponding to the 1/r 2 model.…”

mentioning

confidence: 99%

“…In one dimension, many-body Hamiltonians with pair-potentials of the form 1/r 2 (or its periodic equivalent 1/sin 2 r), where r = (u a −u b ), have exact ground state wave functions of the Jastrow form [2][3][4][5]. It has been…”

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A cross-over from Fermi-liquid to non-Fermi-liquid behaviour in a solvable one-dimensional model

Chen¹,

Muttalib²

1994

J. Phys.: Condens. Matter

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We consider a quantum many-body problem in one-dimension described by a Jastrow type wavefunction, characterized by an exponent λ and a parameter γ. In the limit γ = 0 the model becomes identical to the well known 1/r 2 pair-potential model; γ is shown to be related to the strength of a many body correction to the 1/r 2 interaction. Exact results for the one-particle density matrix are obtained for all γ when λ = 1, for which the 1/r 2 part of the interaction vanishes. We show that with increasing γ, the Fermi liquid state (at γ = 0) crosses over to distinct γ-dependent non-Fermi liquid states, characterized by effective "temperatures".

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“…which is a generalization of the two-particle Calogero-Sutherland model [25]. The relationship between AdS 2 gravity and the Calogero model was first pointed out in [26].…”

Section: Further Reductionmentioning

confidence: 99%

The Asymptotic Dynamics of two-dimensional (anti-)de Sitter Gravity

Brigante¹,

Cacciatori²,

Klemm³

et al. 2002

J. High Energy Phys.

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We show that the asymptotic dynamics of two-dimensional de Sitter or anti-de Sitter Jackiw-Teitelboim (JT) gravity is described by a generalized two-particle Calogero-Sutherland model. This correspondence is established by formulating the JT model of (A)dS gravity in two dimensions as a topological gauge theory, which reduces to a nonlinear 0+1-dimensional sigma model on the boundary of (A)dS space. The appearance of cyclic coordinates allows then a further reduction to the Calogero-Sutherland quantum mechanical model.

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Exact Results for a Quantum Many-Body Problem in One Dimension

Cited by 827 publications

References 15 publications

The spin Sutherland model of type and its associated spin chain

The spin Sutherland model of type and its associated spin chain

A cross-over from Fermi-liquid to non-Fermi-liquid behaviour in a solvable one-dimensional model

The Asymptotic Dynamics of two-dimensional (anti-)de Sitter Gravity

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