Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0609408 · Physical Review B

Spontaneous breaking of the Fermi-surface symmetry in the t−J model: A numerical study

Bernhard Edegger, V. N. Muthukumar, Claudius Gros

Published Oct 19, 2006• 51 citations
arXivHTMLPDF

Abstract

We present a variational Monte Carlo (VMC) study of spontaneous Fermi-surface symmetry breaking in the $t\text{\ensuremath{-}}J$ model. We find that the variational energy of a Gutzwiller projected Fermi sea is lowered by allowing for a finite asymmetry between the $x$ and the $y$ directions. However, the best variational state remains a pure superconducting state with $d$-wave symmetry, as long as the underlying lattice is isotropic. Our VMC results are in good overall agreement with slave boson mean field theory (SBMFT) and renormalized mean field theory (RMFT), although apparent discrepancies do show up in the half-filled limit, revealing some limitations of mean field theories. VMC and complementary RMFT calculations also confirm the SBMFT predictions that many-body interactions can enhance any anisotropy in the underlying crystal lattice. Thus, our results may be of consequence for the description of strongly correlated superconductors with an anisotropic lattice structure.

DOI
10.1103/physrevb.74.165109

Related papers

Spontaneous Fermi Surface Deformation in the Three-Band Hubbard Model: A Variational Monte Carlo Study

Xiao-Jun Zheng, Zhongbing Huang, Liang‐Jian Zou

We perform a variational Monte Carlo study on spontaneous d-wave form Fermi surface deformation ($d$FSD) within the three-band Hubbard model. It is found that the variational energy of a projected Fermi sea is lowered by introducing an anisotropy between the hopping integrals along the x and y directions. Our results show that the $d$FSD state has the strongest tendency at half-filling in the absence of magnetism, and disappears as the hole concentration increases to $n_h\approx 1.15$. This is qualitatively in agreement with the mean field analysis and the exact diagonalization calculation for the one-band models, and provides a qualitative explanation to the "intra-unit-cell" electronic nematicity revealed by the scanning tunneling microscopy. An analysis of the dependence of $d$FSD on the parameters of the three-band model indicates that the copper on-site Coulomb interaction, the nearest-neighbor copper-oxygen repulsion, and the charge-transfer energy have a remarkable positive effect on $d$FSD.

arXiv:1301.1012•Journal of the Physical Society of Japan•Jan 15, 2014•4 citations

Relationship between superconductivity and anisotropy in two-dimensional Hubbard model

Kenji Kobayashi, Hisatoshi Yokoyama

Abstract In connection with the symmetry-breaking phenomena found in cuprate superconductors, we check whether an anisotropy spontaneously appears or not in strongly correlated electrons that exhibit superconductivity and/or antiferromagnetism. A variational Monte Carlo method is applied to the square-lattice Hubbard model (U/t = 12) with diagonal transfer t′. In the trial wave function used, we introduce band renormalization factors including adjustable parameters for the anisotropy corresponding to the fourfold rotational symmetry breaking. It is confirmed that the anisotropy appears in the overdoped regime, where the Fermi-liquid features are predominant. In the underdoped area, the anisotropy does not appear for t′/t = 0 and +0.3, whereas it possibly appears in the underdoped regime for t′/t = −0.3.

Journal of Physics Conference Series•Sep 1, 2019•0 citations

Spontaneous Deformation of the Fermi Surface due to Strong Correlation in the Two-Dimensional t - J Model

Akihiro Himeda, Masao Ogata

The Fermi surface of the two-dimensional t- J model is studied using the variational Monte Carlo method. We study the Gutzwiller-projected d-wave superconducting state with an additional variational parameter t(')(v) corresponding to the next-nearest-neighbor hopping term. It is found that the finite t(')(v)<0 gives the lowest variational energy in the wide range of hole-doping rates. The obtained momentum distribution function shows that the Fermi surface deforms spontaneously. It is also shown that the Van Hove singularity is always located very close to the Fermi energy. Using the Gutzwiller approximation, we show that this deformation is due to the Gutzwiller projection operator or the strong correlation.

arXiv:cond-mat/0003278•Physical Review Letters•Nov 13, 2000•48 citations

Pomeranchuk Instability in Strongly Correlated Hubbard Model

Kenji Kobayashi, Hisatoshi Yokoyama

In connection with the symmetry-breaking phenomena found in cuprate superconductors, the instability toward x-y and (x + y)-(xy) 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.By analyzing a normal (paramagnetic), d x 2 -y 2 -wave superconducting, and antiferromagnetic states for t ′ /t = 0, ±0.3 and 0 ≤ δ ≤ 0.3 (δ: doping rate), we argue that the possibility of Pomeranchuk instability is limited to the normal state with t ′ /t = 0 and 0.05 ≲ δ ≲ 0.20 in the x-y anisotropy.Band-renormalization effects (Fermi-surface changes), which are introduced to each state, play a crucial role for the argument.

International Conference on Strongly Correlated Electron Systems (SCES)•Mar 18, 2020•0 citations

Unidirectional d -wave superconducting domains in the two-dimensional t−J model

Marcin Raczkowski, Manuela Capello, Didier Poilblanc +2 more

Motivated by the recently observed pattern of unidirectional domains in high-${T}_{c}$ superconductors [Y. Kohsaka et al., Science 315, 1380 (2007)], we investigate the emergence of spontaneous modulations in the $d$-wave superconducting resonating valence bond phase using the $t$-$J$ model at $x=1∕8$ doping. Half-filled charge domains separated by four lattice spacings are found to form along one of the crystal axes, leading to modulated superconductivity with out-of-phase $d$-wave order parameters in neighboring domains. Both renormalized mean-field theory and variational Monte Carlo calculations reveal that the energies of modulated and uniform phases are very close to each other.

arXiv:0708.0788•Physical Review B•Oct 19, 2007•114 citations

Variational wave function for an anisotropic single-hole-doped $t$-$J$ ladder

Qing-Rui Wang, Zheng Zhu, Yang Qi +1 more

Based on three general guiding principles, i.e., no double occupancy constraint, accurate description of antiferromagnetism at half-filling, and the precise sign structure of the $t$-$J$ model, a new ground state wave function has been constructed recently [Weng, New J. Phys. 13, 103039 (2011)]. In this paper, we specifically study such kind of variational ground state for the one-hole-doped anisotropic two-leg $t$-$J$ ladder using variational Monte Carlo (VMC) method. The results are then systematically compared with those recently obtained by density matrix renormalization group (DMRG) simulation. An excellent agreement is found between the VMC and DMRG results, including a "quantum critical point" at the anisotropy parameter $α=α_c\approx0.7$ (with the parameters $t/J=3$), and the emergence of charge modulation and momentum (Fermi point) reconstruction at $α>α_c$ due to the quantum interference of the sign structure. In particular, the wave function indicates that a Landau's quasiparticle description remains valid at $αα_c$ due to the breakdown of the one-to-one correspondence of momentum and translational symmetry of the hole. The explicit form of the wave function provides a direct understanding on how the many-body strong correlation effect takes place non-perturbatively in a doped Mott insulator, which sheds interesting light on the two-dimensional case where the same type of wave function was proposed to describe the cuprate superconductor.

arXiv:1509.01260•Sep 3, 2015•7 citations
We present a variational Monte Carlo (VMC) study of spontaneous Fermi-surface symmetry breaking in the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model. We find that the variational energy of a Gutzwiller projected Fermi sea is lowered by allowing for a finite asymmetry between the xxx and the yyy directions. However, the best variational state remains a pure superconducting state with ddd-wave symmetry, as long as the underlying lattice is isotropic. Our VMC results are in good overall agreement with slave boson mean field theory (SBMFT) and renormalized mean field theory (RMFT), although apparent discrepancies do show up in the half-filled limit, revealing some limitations of mean field theories. VMC and complementary RMFT calculations also confirm the SBMFT predictions that many-body interactions can enhance any anisotropy in the underlying crystal lattice. Thus, our results may be of consequence for the description of strongly correlated superconductors with an anisotropic lattice structure.
We perform a variational Monte Carlo study on spontaneous d-wave form Fermi surface deformation (dddFSD) within the three-band Hubbard model. It is found that the variational energy of a projected Fermi sea is lowered by introducing an anisotropy between the hopping integrals along the x and y directions. Our results show that the dddFSD state has the strongest tendency at half-filling in the absence of magnetism, and disappears as the hole concentration increases to nh≈1.15n_h\approx 1.15nh​≈1.15. This is qualitatively in agreement with the mean field analysis and the exact diagonalization calculation for the one-band models, and provides a qualitative explanation to the "intra-unit-cell" electronic nematicity revealed by the scanning tunneling microscopy. An analysis of the dependence of dddFSD on the parameters of the three-band model indicates that the copper on-site Coulomb interaction, the nearest-neighbor copper-oxygen repulsion, and the charge-transfer energy have a remarkable positive effect on dddFSD.
Abstract In connection with the symmetry-breaking phenomena found in cuprate superconductors, we check whether an anisotropy spontaneously appears or not in strongly correlated electrons that exhibit superconductivity and/or antiferromagnetism. A variational Monte Carlo method is applied to the square-lattice Hubbard model (U/t = 12) with diagonal transfer t′. In the trial wave function used, we introduce band renormalization factors including adjustable parameters for the anisotropy corresponding to the fourfold rotational symmetry breaking. It is confirmed that the anisotropy appears in the overdoped regime, where the Fermi-liquid features are predominant. In the underdoped area, the anisotropy does not appear for t′/t = 0 and +0.3, whereas it possibly appears in the underdoped regime for t′/t = −0.3.
The Fermi surface of the two-dimensional t- J model is studied using the variational Monte Carlo method. We study the Gutzwiller-projected d-wave superconducting state with an additional variational parameter t(')(v) corresponding to the next-nearest-neighbor hopping term. It is found that the finite t(')(v)<0 gives the lowest variational energy in the wide range of hole-doping rates. The obtained momentum distribution function shows that the Fermi surface deforms spontaneously. It is also shown that the Van Hove singularity is always located very close to the Fermi energy. Using the Gutzwiller approximation, we show that this deformation is due to the Gutzwiller projection operator or the strong correlation.
In connection with the symmetry-breaking phenomena found in cuprate superconductors, the instability toward x-y and (x + y)-(xy) 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.By analyzing a normal (paramagnetic), d x 2 -y 2 -wave superconducting, and antiferromagnetic states for t ′ /t = 0, ±0.3 and 0 ≤ δ ≤ 0.3 (δ: doping rate), we argue that the possibility of Pomeranchuk instability is limited to the normal state with t ′ /t = 0 and 0.05 ≲ δ ≲ 0.20 in the x-y anisotropy.Band-renormalization effects (Fermi-surface changes), which are introduced to each state, play a crucial role for the argument.
Motivated by the recently observed pattern of unidirectional domains in high-Tc{T}_{c}Tc​ superconductors [Y. Kohsaka et al., Science 315, 1380 (2007)], we investigate the emergence of spontaneous modulations in the ddd-wave superconducting resonating valence bond phase using the ttt-JJJ model at x=1∕8x=1∕8x=1∕8 doping. Half-filled charge domains separated by four lattice spacings are found to form along one of the crystal axes, leading to modulated superconductivity with out-of-phase ddd-wave order parameters in neighboring domains. Both renormalized mean-field theory and variational Monte Carlo calculations reveal that the energies of modulated and uniform phases are very close to each other.
Variational wave function for an anisotropic single-hole-doped ttt-JJJ ladder
Based on three general guiding principles, i.e., no double occupancy constraint, accurate description of antiferromagnetism at half-filling, and the precise sign structure of the ttt-JJJ model, a new ground state wave function has been constructed recently [Weng, New J. Phys. 13, 103039 (2011)]. In this paper, we specifically study such kind of variational ground state for the one-hole-doped anisotropic two-leg ttt-JJJ ladder using variational Monte Carlo (VMC) method. The results are then systematically compared with those recently obtained by density matrix renormalization group (DMRG) simulation. An excellent agreement is found between the VMC and DMRG results, including a "quantum critical point" at the anisotropy parameter α=αc≈0.7α=α_c\approx0.7α=αc​≈0.7 (with the parameters t/J=3t/J=3t/J=3), and the emergence of charge modulation and momentum (Fermi point) reconstruction at α>αcα>α_cα>αc​ due to the quantum interference of the sign structure. In particular, the wave function indicates that a Landau's quasiparticle description remains valid at ααcαα_cααc​ due to the breakdown of the one-to-one correspondence of momentum and translational symmetry of the hole. The explicit form of the wave function provides a direct understanding on how the many-body strong correlation effect takes place non-perturbatively in a doped Mott insulator, which sheds interesting light on the two-dimensional case where the same type of wave function was proposed to describe the cuprate superconductor.