# Orbital currents and charge density waves in a generalized Hubbard ladder

## Abstract

We study a generalized Hubbard model on the two-leg ladder at zero temperature, focusing on a parameter region with staggered flux (SF)/d-density wave (DDW) order. To guide our numerical calculations, we first investigate the location of a SF/DDW phase in the phase diagram of the half-filled weakly interacting ladder using a perturbative renormalization group (RG) and bosonization approach. For hole doping {delta} away from half-filling, finite-system density-matrix renormalization-group (DMRG) calculations are used to study ladders with up to 200 rungs for intermediate-strength interactions. In the doped SF/DDW phase, the staggered rung current and the rung electron density both show periodic spatial oscillations, with characteristic wavelengths 2/{delta} and 1/{delta}, respectively, corresponding to ordering wavevectors 2k {sub F} and 4k {sub F} for the currents and densities, where 2k {sub F} = {pi} (1 - {delta}). The density minima are located at the anti-phase domain walls of the staggered current. For sufficiently large dopings, SF/DDW order is suppressed. The rung density modulation also exists in neighboring phases where currents decay exponentially. We show that most of the DMRG results can be qualitatively understood from weak-coupling RG/bosonization arguments. However, while these arguments seem to suggest a crossover from non-decaying correlations to power-law decaymore »

- Authors:

- Department of Physics and Astronomy, University of California, Los Angeles, CA 90095 (United States) and Department of Physics, University of Queensland, Brisbane, Qld 4072 (Australia). E-mail: fjaerestad@physics.uq.edu.au
- Department of Physics, Brown University, Providence, RI 02912 (United States)
- Institute for Theoretical Physics C, RWTH Aachen, D-52056 Aachen (Germany)

- Publication Date:

- OSTI Identifier:
- 20767003

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics (New York); Journal Volume: 321; Journal Issue: 4; Other Information: DOI: 10.1016/j.aop.2005.08.005; PII: S0003-4916(05)00137-5; Copyright (c) 2005 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSON EXPANSION; CHARGE DENSITY; CORRELATIONS; DENSITY MATRIX; ELECTRON DENSITY; FOCUSING; HOLES; HUBBARD MODEL; INTERACTIONS; MODULATION; OSCILLATIONS; PERIODICITY; PHASE DIAGRAMS; RENORMALIZATION; WAVELENGTHS

### Citation Formats

```
Fjaerestad, J.O., Marston, J.B., and Schollwoeck, U.
```*Orbital currents and charge density waves in a generalized Hubbard ladder*. United States: N. p., 2006.
Web. doi:10.1016/j.aop.2005.08.005.

```
Fjaerestad, J.O., Marston, J.B., & Schollwoeck, U.
```*Orbital currents and charge density waves in a generalized Hubbard ladder*. United States. doi:10.1016/j.aop.2005.08.005.

```
Fjaerestad, J.O., Marston, J.B., and Schollwoeck, U. Sat .
"Orbital currents and charge density waves in a generalized Hubbard ladder". United States.
doi:10.1016/j.aop.2005.08.005.
```

```
@article{osti_20767003,
```

title = {Orbital currents and charge density waves in a generalized Hubbard ladder},

author = {Fjaerestad, J.O. and Marston, J.B. and Schollwoeck, U.},

abstractNote = {We study a generalized Hubbard model on the two-leg ladder at zero temperature, focusing on a parameter region with staggered flux (SF)/d-density wave (DDW) order. To guide our numerical calculations, we first investigate the location of a SF/DDW phase in the phase diagram of the half-filled weakly interacting ladder using a perturbative renormalization group (RG) and bosonization approach. For hole doping {delta} away from half-filling, finite-system density-matrix renormalization-group (DMRG) calculations are used to study ladders with up to 200 rungs for intermediate-strength interactions. In the doped SF/DDW phase, the staggered rung current and the rung electron density both show periodic spatial oscillations, with characteristic wavelengths 2/{delta} and 1/{delta}, respectively, corresponding to ordering wavevectors 2k {sub F} and 4k {sub F} for the currents and densities, where 2k {sub F} = {pi} (1 - {delta}). The density minima are located at the anti-phase domain walls of the staggered current. For sufficiently large dopings, SF/DDW order is suppressed. The rung density modulation also exists in neighboring phases where currents decay exponentially. We show that most of the DMRG results can be qualitatively understood from weak-coupling RG/bosonization arguments. However, while these arguments seem to suggest a crossover from non-decaying correlations to power-law decay at a length scale of order 1/{delta}, the DMRG results are consistent with a true long-range order scenario for the currents and densities.},

doi = {10.1016/j.aop.2005.08.005},

journal = {Annals of Physics (New York)},

number = 4,

volume = 321,

place = {United States},

year = {Sat Apr 15 00:00:00 EDT 2006},

month = {Sat Apr 15 00:00:00 EDT 2006}

}