Title:	Determinant Quantum Monte Carlo study of odd-frequency pairing state in quasi one-dimensional Hubbard model
DNr:	SNIC 2018/3-507
Project Type:	SNIC Medium Compute
Principal Investigator:	Konstantin Zarembo <konstantin.zarembo@su.se>
Affiliation:	NORDITA
Duration:	2018-11-01 – 2019-05-01
Classification:	10304
Keywords:

Abstract

An odd frequency pairing state was first proposed by Berezinsky [1] as a model of superfluid He3. Such states are characterized by pairing wave-functions odd in frequency and thus different from the s, p, d, ...,-wave pairing states found in various superconductors. Being novel pairing states, not yet found in the lab, it would be of great interest to find a bulk model where this exotic pairing shows up spontaneously. An odd-frequency, singlet, odd parity pairing state (OSO) has been predicted in quasi one-dimensional Hubbard models [3, 4]. These states were found using two different perturbative methods: the random phase approximation (RPA) and the fluctuation exchange approximation. The interaction of the Hubbard model is relevant in one dimension and it can thus not be studied perturbatively there. The above results are found using perturbative methods and the OSO states appear upon approaching one-dimension and one should treat these results with some care until a more rigorous calculation has been performed. Numerical studies of the Hubbard model in the strong coupling regime are challenging. Without perturbation theory we have to resort to either variational methods such as tensor product states [5] or determinant quantum Monte Carlo (DQMC) [6]. DQMC has been used to study the OSO pairing state in the Hubbard model already in 1993 [7]. We propose to perform DQMC calculations similar to the one in [7] but on non-square lattices to see whether the OSO state discussed above persists beyond perturbation theory. The system treated perturbatively in [3] is not directly amenable to a DQMC calculation. The system size (128 × 64) is much too large and the diagonal hoppings break particle-hole symmetry and result in a fermion sign problem [8]. We have reproduced some of the results in [3] in order to investigate whether it is possible to find the same OSO state in a simpler system, that is amenable to DQMC. The OSO state dominates in the one-dimensional limit, however, [3] only shows results for r = ty,2/tx down to r = .1. Extending these results to the one-dimensional limit we find that the OSO state persists. This means that turning off the diagonal hopping we necessarily still have a region where the OSO state dominates. The model is one-dimensional for r = 0 so for r = 0 we can use a one-dimensional system of size 128 × 1. For small r we expect “inter-chain” hopping to be suppressed and a small size in the y direction to be sufficient. We have used RPA to study a smaller system of size 32*8 without diagonal hoppings which is amenable to DQMC. The OSO state is still seen to dominate in the r → 0 limit. We thus find that the OSO state of [3] persists (when studied using RPA) in a region that is sign-problem free and is amenable to DQMC. [1] VL Berezinskii. New model of the anisotropic phase of superfluid he3. Jetp Lett, 20(9):287–289, 1974. [2] Jacob Linder and Alexander V Balatsky. Odd-frequency superconductivity. arXiv preprint arXiv:1709.03986, 2017. [3] Keisuke Shigeta, Seiichiro Onari, Keiji Yada, and Yukio Tanaka. Theory of odd-frequency pairings on a quasi-one-dimensional lattice in the hubbard model. Phys. Rev. B, 79:174507, May 2009. [4] Keisuke Shigeta, Yukio Tanaka, Kazuhiko Kuroki, Seiichiro Onari, and Hirohito Aizawa. Competi- tion of pairing symmetries and a mechanism for berezinskii pairing in quasi-one-dimensional systems. Phys. Rev. B, 83:140509, Apr 2011. [5] Philippe Corboz. Improved energy extrapolation with infinite projected entangled-pair states applied to the two-dimensional hubbard model. Phys. Rev. B, 93:045116, Jan 2016. [6] S. R. White, D. J. Scalapino, R. L. Sugar, E. Y. Loh, J. E. Gubernatis, and R. T. Scalettar. Numerical study of the two-dimensional hubbard model. Phys. Rev. B, 40:506–516, Jul 1989. [7] N. Bulut, D. J. Scalapino, and S. R. White. Bethe-salpeter eigenvalues and amplitudes for the half-filled two-dimensional hubbard model. Phys. Rev. B, 47:14599–14602, Jun 1993. [8] E. Y. Loh, J. E. Gubernatis, R. T. Scalettar, S. R. White, D. J. Scalapino, and R. L. Sugar. Sign problem in the numerical simulation of many-electron systems. Phys. Rev. B, 41:9301–9307, May 1990.