## Symmetry-conserving purification of quantum states within the density matrix renormalization group

## Abstract

The density matrix renormalization group (DMRG) algorithm was originally designed to efficiently compute the zero-temperature or ground-state properties of one-dimensional strongly correlated quantum systems. The development of the algorithm at finite temperature has been a topic of much interest, because of the usefulness of thermodynamics quantities in understanding the physics of condensed matter systems, and because of the increased complexity associated with efficiently computing temperature-dependent properties. The ancilla method is a DMRG technique that enables the computation of these thermodynamic quantities. In this paper, we review the ancilla method, and improve its performance by working on reduced Hilbert spaces and using canonical approaches. Furthermore we explore its applicability beyond spins systems to t-J and Hubbard models.

- Authors:

- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1236593

- Alternate Identifier(s):
- OSTI ID: 1236403

- Grant/Contract Number:
- AC05-00OR22725

- Resource Type:
- Accepted Manuscript

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

- Additional Journal Information:
- Journal Volume: 93; Journal Issue: 4; Journal ID: ISSN 0163-1829

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Nocera, Alberto, and Alvarez, Gonzalo. Symmetry-conserving purification of quantum states within the density matrix renormalization group. United States: N. p., 2016.
Web. doi:10.1103/PhysRevB.93.045137.
```

```
Nocera, Alberto, & Alvarez, Gonzalo. Symmetry-conserving purification of quantum states within the density matrix renormalization group. United States. doi:10.1103/PhysRevB.93.045137.
```

```
Nocera, Alberto, and Alvarez, Gonzalo. Thu .
"Symmetry-conserving purification of quantum states within the density matrix renormalization group". United States. doi:10.1103/PhysRevB.93.045137. https://www.osti.gov/servlets/purl/1236593.
```

```
@article{osti_1236593,
```

title = {Symmetry-conserving purification of quantum states within the density matrix renormalization group},

author = {Nocera, Alberto and Alvarez, Gonzalo},

abstractNote = {The density matrix renormalization group (DMRG) algorithm was originally designed to efficiently compute the zero-temperature or ground-state properties of one-dimensional strongly correlated quantum systems. The development of the algorithm at finite temperature has been a topic of much interest, because of the usefulness of thermodynamics quantities in understanding the physics of condensed matter systems, and because of the increased complexity associated with efficiently computing temperature-dependent properties. The ancilla method is a DMRG technique that enables the computation of these thermodynamic quantities. In this paper, we review the ancilla method, and improve its performance by working on reduced Hilbert spaces and using canonical approaches. Furthermore we explore its applicability beyond spins systems to t-J and Hubbard models.},

doi = {10.1103/PhysRevB.93.045137},

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

number = 4,

volume = 93,

place = {United States},

year = {2016},

month = {1}

}

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