# Critical exponents for the sinh-cosh interaction model in the zero sector

## Abstract

In this paper, we continue our investigation of a one-dimensional, two-component, quantum many-body system in which like particles interact with a pair potential {ital s}({ital s}+1)/sinh{sup 2}({ital r}), while unlike particles interact with a pair potential {minus}{ital s}({ital s}+1)/cosh{sup 2}({ital r}). For an equal number of particles of the two components, the ground state for {ital s}{gt}0 corresponds to an antiferromagnet/insulator. Excitations consist of a gapless pair-hole--pair continuum, a two-particle continuum with gap and excitons with gap. For {minus}1{lt}{ital s}{lt}0, the system has two gapless excitations---a particle-hole continuum and a two-spin-wave continuum. Using finite-size scaling methods of conformal field theory, we calculate the asymptotic expressions and critical exponents for correlation functions of these gapless excitations at zero temperature. The conformal structure is closely related to the Hubbard model with repulsive on-site interaction.

- Authors:

- Physics Department, University of Utah, Salt Lake City, Utah 84112 (United States)

- Publication Date:

- OSTI Identifier:
- 142610

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review, B: Condensed Matter

- Additional Journal Information:
- Journal Volume: 49; Journal Issue: 10; Other Information: PBD: 1 Mar 1994

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 66 PHYSICS; MANY-BODY PROBLEM; COLLECTIVE EXCITATIONS; QUANTIZATION; MATHEMATICAL MODELS; HUBBARD MODEL; ANTIFERROMAGNETISM; SPIN WAVES; HOLES; SCALING; CONFORMAL INVARIANCE

### Citation Formats

```
Roemer, R.A., and Sutherland, B..
```*Critical exponents for the sinh-cosh interaction model in the zero sector*. United States: N. p., 1994.
Web. doi:10.1103/PhysRevB.49.6779.

```
Roemer, R.A., & Sutherland, B..
```*Critical exponents for the sinh-cosh interaction model in the zero sector*. United States. doi:10.1103/PhysRevB.49.6779.

```
Roemer, R.A., and Sutherland, B.. Tue .
"Critical exponents for the sinh-cosh interaction model in the zero sector". United States. doi:10.1103/PhysRevB.49.6779.
```

```
@article{osti_142610,
```

title = {Critical exponents for the sinh-cosh interaction model in the zero sector},

author = {Roemer, R.A. and Sutherland, B.},

abstractNote = {In this paper, we continue our investigation of a one-dimensional, two-component, quantum many-body system in which like particles interact with a pair potential {ital s}({ital s}+1)/sinh{sup 2}({ital r}), while unlike particles interact with a pair potential {minus}{ital s}({ital s}+1)/cosh{sup 2}({ital r}). For an equal number of particles of the two components, the ground state for {ital s}{gt}0 corresponds to an antiferromagnet/insulator. Excitations consist of a gapless pair-hole--pair continuum, a two-particle continuum with gap and excitons with gap. For {minus}1{lt}{ital s}{lt}0, the system has two gapless excitations---a particle-hole continuum and a two-spin-wave continuum. Using finite-size scaling methods of conformal field theory, we calculate the asymptotic expressions and critical exponents for correlation functions of these gapless excitations at zero temperature. The conformal structure is closely related to the Hubbard model with repulsive on-site interaction.},

doi = {10.1103/PhysRevB.49.6779},

journal = {Physical Review, B: Condensed Matter},

number = 10,

volume = 49,

place = {United States},

year = {1994},

month = {3}

}