Two-dimensional massive integrable models on a torus (original) (raw)
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Arxiv preprint cond-mat/0412532, 2004
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Integrable Models in Condensed Matter Physics
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A path-integral formalism for the one-dimensional Hubbard model in the strong-coupling regime, which is equivalent to the t-J model in t/U expansion but without any explicit constraint, is developed. Based on this formalism, the zero-temperature properties of the Hubbard chain are systematically studied. In the infinite-U limit, the charge and spin degrees of freedom are shown to be completely separated. Such a separation at U=~p rovides a controllable perturbative scheme to study the strongcoupling case. In the large-U regime, the spin degree of freedom is represented by a "squeezed" Heisenberg chain. We solve the {squeezed) Heisenberg chain by introducing a soliton representation. Both the charge and spin excitations are found to agree well with the exact solution. The bare electron (hole) is shown to be a composite particle of these basic excitations, i.e. , holon and spinon, together with a nonlocal string field. This string field makes the electron behave like a "semion" and plays an important role in determining various correlation functions. We analytically derive the asymptotic forms of the spinspin and density-density correlation functions as well as the single-electron and the pair-electron Green's functions. The implications of the present work to the two-dimensional model are discussed.
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We explain how to incorporate the action of local integrals of motion into the fermionic basis for the sine-Gordon model and its UV CFT. The examples up to the level 4 are presented. Numerical computation support the results. Possible applications are discussed.
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T overlineT\overline{T}overlineT-flow effects on torus partition functions
Journal of High Energy Physics, 2021
In this paper, we investigate the partition functions of conformal field theories (CFTs) with the ToverlineT\overline{T}overlineT T ¯ deformation on a torus in terms of the perturbative QFT approach. In Lagrangian path integral formalism, the first- and second-order deformations to the partition functions of 2D free bosons, free Dirac fermions, and free Majorana fermions on a torus are obtained. The corresponding Lagrangian counterterms in these theories are also discussed. The first two orders of the deformed partition functions and the first-order vacuum expectation value (VEV) of the first quantum KdV charge obtained by the perturbative QFT approach are consistent with results obtained by the Hamiltonian formalism in literature.