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International Conference on Strongly Correlated Electron Systems (SCES)

Effect of Diagonal Hopping on Staggered Flux State in Square-Lattice Hubbard model

Hisatoshi Yokoyama, Shun Tamura, Masao Ogata

Published Jun 16, 2014• 2 citations
Publisher

Abstract

In view of the pseudogap in underdoped cuprate superconductors, we study the stability of a staggered flux state SF against the conventional metallic state as the normal state which underlies the d-wave superconductivity, using a variational Monte Carlo method. We focus on the effect of diagonal hopping term (t 0 ) in the square-lattice Hubbard model on the stability of SF. The results are

DOI
10.7566/jpscp.3.012029

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In view of the pseudogap in underdoped cuprate superconductors, we study the stability of a staggered flux state SF against the conventional metallic state as the normal state which underlies the d-wave superconductivity, using a variational Monte Carlo method. We focus on the effect of diagonal hopping term (t 0 ) in the square-lattice Hubbard model on the stability of SF. The results are
With cuprate superconductors in mind, we check whether the d -wave superconducting ( d SC) state coexists with or excludes the staggered flux (SF) state, which was revealed to be the strong candidate for the pseudogap state. To this end, we use a variational Monte Carlo method for the square Hubbard model with diagonal transfer t '. In the trial wave function, d SC and SF orders coexist, which allows a continuous description of their interplay; essential factors for Mott physics and band renormalization are also included. It is found that the SF state does not coexist with d SC and is unstable for U/t = 12 regardless of the value of t'/t within the present work.
Abstract In connection with the symmetry-breaking phenomena found in cuprate superconductors, the instability toward x−y and (x + y)−(x − y) anisotropy (Pomeranchuk instability) is studied for a strongly correlated Hubbard model (U/t = 12) on a square lattice with the next-nearest-neighbor transfer t′ using a variational Monte Carlo method. As a variational function, a staggered flux state ΨSF is considered, which is a candidate for the pseudogap state in cuprates. ΨSF is stabilized in a underdoped regime and reduced to the normal state (projected Fermi sea) for larger doping area. By analyzing ΨSF for t′/t = 0, ±0.3, we argue that the appearance of Pomeranchuk instability is limited to the normal state with t′/t = 0 and 0.08 ≤ δ ≤ 0.20 (σ: doping rate) in the x−y anisotropy. Band-renormalization effects (Fermi-surface modification) owing to strong correlations play a crucial role for the argument.
The stability of a staggered flux (SF) or d-density wave state is studied in a d-p model using a variational Monte Carlo (VMC) method. This state possesses a local circular current and possibly causes the pseudogap phase in high-Tc cuprate superconductors. We introduce into the trial function a configuration dependent phase factor, which was recently shown to be indispensable to stabilize current-carrying states. We pay attention to the energy gain as a function of adjacent O-O hopping and Cu-site coulomb repulsion U. It is found the SF state becomes stable for hole doping rates of and , owing to the reduction in kinetic energy, but seems fragile because the energy gain rapidly decays on doping holes for any . The loop current tends to increase as increases.
With cuprate superconductors in mind, we check whether the d -wave superconducting ( d SC) state coexists with or excludes the staggered flux (SF) state, which was revealed to be a strong candidate for the pseudogap state. To this end, we use a variational Monte Carlo method for the square-lattice t - J model with diagonal transfer t '. We construct a trial wave function which can simultaneously represent d SC and SF orders for a continuous description of their interplay. Furthermore, a band renormalization effect is introduced into both orders independently. It is found that the SF state does not coexist with d SC and is unstable for a wide area in the parameter space. However, a strange state having both SF and antiferromagnetic orders is found to be stable for very low doping rate.
Most studies of square-lattice Hubbard models in view of cuprate superconductors hitherto have neglected a band-renormalization effect (BRE) owing to strong electron correlation, especially, for an antiferromagnetic (AF) order. In this study, we introduce BRE into a d -wave superconducting and an AF states independently in the framework of many-body variation theory. It is found that, in sharp contrast to usual understandings, energy of an AF state is sizably reduced by BRE, and the AF area in the ground-state phase diagram is greatly expanded to cover the whole underdoped regime. The AF state with BRE exhibits distinct features according as the value of diagonal hopping ratio t ′/ t is greater or less than t ′/ t ∼ – 0.05.
In view of strongly interacting bosons in an optical lattice with a large gauge field, we study phase transitions in a two-dimensional Bose-Hubbard model with a staggered flux, on the basis of variational Monte Carlo calculations. Inthe trial states,besides typical onsite and intersite correlation factors, we introduce a configuration-dependent phase factor,which was recently found essential for treating current-carrying states. It is found that this phase factor is qualitativelyvitalfordescribing a Mott insulating (MI) state in the present model. Thereby, the Peierls phasesattached in relevant hopping processes are cancelled out. As a result, local currents completely suppressed in MI states, namely, a chiral Mott state does not appear for the square lattice, in contrast tothecorresponding two-leg ladder model. In addition, we discuss other features of the first-order superfluid-MI transition in this model.