International Conference on Strongly Correlated Electron Systems (SCES)

Pomeranchuk Instability in Strongly Correlated Hubbard Model

Kenji Kobayashi, Hisatoshi Yokoyama

Published Mar 18, 2020• 0 citations

Abstract

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.

DOI: 10.7566/jpscp.30.011046

Related papers

Possibility of Pomeranchuk instability in staggered flux state

Kenji Kobayashi, Hisatoshi Yokoyama

Journal of Physics Conference SeriesJul 1, 20200 citations

Relationship between superconductivity and anisotropy in two-dimensional Hubbard model

Kenji Kobayashi, Hisatoshi Yokoyama

Journal of Physics Conference SeriesSep 1, 20190 citations

d -Wave Superconductivity and Pomeranchuk Instability in the Two-Dimensional Hubbard Model

Christoph J. Halboth, Walter Metzner

arXiv:cond-mat/0003349Physical Review LettersDec 11, 2000476 citations

Interplay of Pomeranchuk instability and superconductivity in the two-dimensional repulsive Hubbard model

Motoharu Kitatani, Naoto Tsuji, Hideo Aoki

arXiv:1609.05759Physical review. B./Physical review. BFeb 3, 201724 citations

Band-renormalization Effect on Relationship between Superconductivity and Antiferromagnetism in t-J Model

Kenji Kobayashi, R. Sato, H. Yokoyama

Physics ProcediaJan 1, 20162 citations

Band-Renormalization Effect on Superconductivity and Antiferromagnetism in Two-Dimensional t–J Model

Ryo Sato, Hisatoshi Yokoyama

The coexistence or exclusivity of $d_{x^{2} - y^{2}}$-wave superconducting (d-SC) and antiferromagnetic (AF) orders and instability toward phase separation (PS) are reconsidered for the square-lattice t–J model with the diagonal transfer (t′) term near half filling. To reliably treat the strong correlation including the local constraint of no double occupancy, we use a variational Monte Carlo method, in which the band-renormalization effect (BRE) is also incorporated. The results are compared with those recently obtained for the corresponding Hubbard model [J. Phys. Soc. Jpn. 85, 074701 (2016)]. It is found that BRE has a very strong effect on the AF order and greatly modifies the ground-state phase diagram in the t′–δ space (δ: doping rate) proposed in previous studies, especially for large |t′/t|. In a wide range of t′/t (|t′/t| ≤ 0.5) and for any underdoped δ ($ \lesssim $ 0.15), the AF order arises for J/t = 0.3, similarly to in the Hubbard model. In contrast with the Hubbard model, however, the d-SC order also arises down to small δ in a wide range of t′/t ($ \gtrsim $ −0.2) and coexists with the AF order even for t′/t < 0 (type-II AF regime). Furthermore, there is no instability toward PS for any t′/t and δ for J/t = 0.3.

Journal of the Physical Society of JapanOct 3, 20184 citations

International Conference on Strongly Correlated Electron Systems (SCES)

Pomeranchuk Instability in Strongly Correlated Hubbard Model

Kenji Kobayashi, Hisatoshi Yokoyama

Published Mar 18, 2020• 0 citations

Publisher

Abstract

DOI: 10.7566/jpscp.30.011046

Related papers

Possibility of Pomeranchuk instability in staggered flux state

Kenji Kobayashi, Hisatoshi Yokoyama

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.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.

Journal of Physics Conference SeriesJul 1, 20200 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.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 SeriesSep 1, 20190 citations

d -Wave Superconductivity and Pomeranchuk Instability in the Two-Dimensional Hubbard Model

Christoph J. Halboth, Walter Metzner

We present a systematic stability analysis for the two-dimensional Hubbard model, which is based on a new renormalization group method for interacting Fermi systems. The flow of effective interactions and susceptibilities confirms the expected existence of a d-wave pairing instability driven by antiferromagnetic spin fluctuations. More unexpectedly, we find that strong forward scattering interactions develop which may lead to a Pomeranchuk instability breaking the tetragonal symmetry of the Fermi surface.We present a systematic stability analysis for the two-dimensional Hubbard model, which is based on a new renormalization group method for interacting Fermi systems. The flow of effective interactions and susceptibilities confirms the expected existence of a d-wave pairing instability driven by antiferromagnetic spin fluctuations. More unexpectedly, we find that strong forward scattering interactions develop which may lead to a Pomeranchuk instability breaking the tetragonal symmetry of the Fermi surface.

arXiv:cond-mat/0003349Physical Review LettersDec 11, 2000476 citations

Interplay of Pomeranchuk instability and superconductivity in the two-dimensional repulsive Hubbard model

Motoharu Kitatani, Naoto Tsuji, Hideo Aoki

Interplay of Pomeranchuk instability (spontaneous symmetry breaking of the Fermi surface) and $d$ -wave superconductivity is studied for the repulsive Hubbard model on the square lattice with the dynamical mean-field theory combined with the fluctuation exchange approximation (FLEX+DMFT). We show that the fourfold symmetric Fermi surface becomes unstable against a spontaneous distortion into twofold near the van Hove filling, where the symmetry of superconductivity coexisting with the Pomeranchuk-distorted Fermi surface is modified from the $d$ -wave pairing to the $(d+s)$ wave. By systematically shifting the position of van Hove filling with varied second- and third-neighbor hoppings, we find that the transition temperature ${T}_{\mathrm{c}}^{\mathrm{PI}}$ for the Pomeranchuk instability is more sensitively affected by the position of van Hove filling than the superconducting ${T}_{\mathrm{c}}^{\mathrm{SC}}$ . This implies that the filling region for strong Pomeranchuk instability and that for the ${T}_{\mathrm{c}}^{\mathrm{SC}}$ dome can be separated, and that Pomeranchuk instability can appear even if the peak of ${T}_{\mathrm{c}}^{\mathrm{PI}}$ is lower than the peak of ${T}_{\mathrm{c}}^{\mathrm{SC}}$ . An interesting finding is that the Fermi surface distortion can enhance the superconducting ${T}_{\mathrm{c}}^{\mathrm{SC}}$ in the overdoped regime, which is explained with a perturbational picture for small distortions.Interplay of Pomeranchuk instability (spontaneous symmetry breaking of the Fermi surface) and $d$-wave superconductivity is studied for the repulsive Hubbard model on the square lattice with the dynamical mean-field theory combined with the fluctuation exchange approximation (FLEX+DMFT). We show that the fourfold symmetric Fermi surface becomes unstable against a spontaneous distortion into twofold near the van Hove filling, where the symmetry of superconductivity coexisting with the Pomeranchuk-distorted Fermi surface is modified from the $d$-wave pairing to the $(d+s)$ wave. By systematically shifting the position of van Hove filling with varied second- and third-neighbor hoppings, we find that the transition temperature ${T}_{\mathrm{c}}^{\mathrm{PI}}$ for the Pomeranchuk instability is more sensitively affected by the position of van Hove filling than the superconducting ${T}_{\mathrm{c}}^{\mathrm{SC}}$. This implies that the filling region for strong Pomeranchuk instability and that for the ${T}_{\mathrm{c}}^{\mathrm{SC}}$ dome can be separated, and that Pomeranchuk instability can appear even if the peak of ${T}_{\mathrm{c}}^{\mathrm{PI}}$ is lower than the peak of ${T}_{\mathrm{c}}^{\mathrm{SC}}$. An interesting finding is that the Fermi surface distortion can enhance the superconducting ${T}_{\mathrm{c}}^{\mathrm{SC}}$ in the overdoped regime, which is explained with a perturbational picture for small distortions.

arXiv:1609.05759Physical review. B./Physical review. BFeb 3, 201724 citations

Band-renormalization Effect on Relationship between Superconductivity and Antiferromagnetism in t-J Model

Kenji Kobayashi, R. Sato, H. Yokoyama

Having cuprate superconductors in mind, we study a band-renormalization effect on a coexisting state of antiferromagnetism (AF) and superconductivity (SC) in a t-J model on a square lattice with a diagonal transfer t ′ and three-site hopping terms, using a variational Monte Carlo method. It is found that this t-J model with t ′/ t = –0.3 exhibits coexistence of AF and SC orders in lightly doped regime and robust SC for a wide range of doping rate δ . This result contrasts with the previous results of a large- U/t Hubbard model, in which the two orders are mutually exclusive and a coexisting state does not appear; the SC state appears only in heavily doped regime (δ≳ 0.2), after the pure AF state vanishes at δ ∼ 0.2.Having cuprate superconductors in mind, we study a band-renormalization effect on a coexisting state of antiferromagnetism (AF) and superconductivity (SC) in a t-J model on a square lattice with a diagonal transfer t ′ and three-site hopping terms, using a variational Monte Carlo method. It is found that this t-J model with t ′/ t = –0.3 exhibits coexistence of AF and SC orders in lightly doped regime and robust SC for a wide range of doping rate δ . This result contrasts with the previous results of a large- U/t Hubbard model, in which the two orders are mutually exclusive and a coexisting state does not appear; the SC state appears only in heavily doped regime (δ≳ 0.2), after the pure AF state vanishes at δ ∼ 0.2.

Physics ProcediaJan 1, 20162 citations

Band-Renormalization Effect on Superconductivity and Antiferromagnetism in Two-Dimensional t–J Model

Ryo Sato, Hisatoshi Yokoyama

The coexistence or exclusivity of $d_{x^{2} - y^{2}}$ -wave superconducting (d-SC) and antiferromagnetic (AF) orders and instability toward phase separation (PS) are reconsidered for the square-lattice t–J model with the diagonal transfer (t′) term near half filling. To reliably treat the strong correlation including the local constraint of no double occupancy, we use a variational Monte Carlo method, in which the band-renormalization effect (BRE) is also incorporated. The results are compared with those recently obtained for the corresponding Hubbard model [J. Phys. Soc. Jpn. 85, 074701 (2016)]. It is found that BRE has a very strong effect on the AF order and greatly modifies the ground-state phase diagram in the t′–δ space (δ: doping rate) proposed in previous studies, especially for large |t′/t|. In a wide range of t′/t (|t′/t| ≤ 0.5) and for any underdoped δ ( $\lesssim$ 0.15), the AF order arises for J/t = 0.3, similarly to in the Hubbard model. In contrast with the Hubbard model, however, the d-SC order also arises down to small δ in a wide range of t′/t ( $\gtrsim$ −0.2) and coexists with the AF order even for t′/t < 0 (type-II AF regime). Furthermore, there is no instability toward PS for any t′/t and δ for J/t = 0.3.The coexistence or exclusivity of $d_{x^{2} - y^{2}}$-wave superconducting (d-SC) and antiferromagnetic (AF) orders and instability toward phase separation (PS) are reconsidered for the square-lattice t–J model with the diagonal transfer (t′) term near half filling. To reliably treat the strong correlation including the local constraint of no double occupancy, we use a variational Monte Carlo method, in which the band-renormalization effect (BRE) is also incorporated. The results are compared with those recently obtained for the corresponding Hubbard model [J. Phys. Soc. Jpn. 85, 074701 (2016)]. It is found that BRE has a very strong effect on the AF order and greatly modifies the ground-state phase diagram in the t′–δ space (δ: doping rate) proposed in previous studies, especially for large |t′/t|. In a wide range of t′/t (|t′/t| ≤ 0.5) and for any underdoped δ ($ \lesssim $ 0.15), the AF order arises for J/t = 0.3, similarly to in the Hubbard model. In contrast with the Hubbard model, however, the d-SC order also arises down to small δ in a wide range of t′/t ($ \gtrsim $ −0.2) and coexists with the AF order even for t′/t < 0 (type-II AF regime). Furthermore, there is no instability toward PS for any t′/t and δ for J/t = 0.3.

Journal of the Physical Society of JapanOct 3, 20184 citations

Interplay of Pomeranchuk instability (spontaneous symmetry breaking of the Fermi surface) and

d

-wave superconductivity is studied for the repulsive Hubbard model on the square lattice with the dynamical mean-field theory combined with the fluctuation exchange approximation (FLEX+DMFT). We show that the fourfold symmetric Fermi surface becomes unstable against a spontaneous distortion into twofold near the van Hove filling, where the symmetry of superconductivity coexisting with the Pomeranchuk-distorted Fermi surface is modified from the

d

-wave pairing to the

(d+s)

wave. By systematically shifting the position of van Hove filling with varied second- and third-neighbor hoppings, we find that the transition temperature

{T}_{\mathrm{c}}^{\mathrm{PI}}

for the Pomeranchuk instability is more sensitively affected by the position of van Hove filling than the superconducting

{T}_{\mathrm{c}}^{\mathrm{SC}}

. This implies that the filling region for strong Pomeranchuk instability and that for the

{T}_{\mathrm{c}}^{\mathrm{SC}}

dome can be separated, and that Pomeranchuk instability can appear even if the peak of

{T}_{\mathrm{c}}^{\mathrm{PI}}

is lower than the peak of

{T}_{\mathrm{c}}^{\mathrm{SC}}

. An interesting finding is that the Fermi surface distortion can enhance the superconducting

{T}_{\mathrm{c}}^{\mathrm{SC}}

in the overdoped regime, which is explained with a perturbational picture for small distortions.

The coexistence or exclusivity of

d_{x^{2} - y^{2}}

-wave superconducting (d-SC) and antiferromagnetic (AF) orders and instability toward phase separation (PS) are reconsidered for the square-lattice t–J model with the diagonal transfer (t′) term near half filling. To reliably treat the strong correlation including the local constraint of no double occupancy, we use a variational Monte Carlo method, in which the band-renormalization effect (BRE) is also incorporated. The results are compared with those recently obtained for the corresponding Hubbard model [J. Phys. Soc. Jpn. 85, 074701 (2016)]. It is found that BRE has a very strong effect on the AF order and greatly modifies the ground-state phase diagram in the t′–δ space (δ: doping rate) proposed in previous studies, especially for large |t′/t|. In a wide range of t′/t (|t′/t| ≤ 0.5) and for any underdoped δ (

\lesssim

0.15), the AF order arises for J/t = 0.3, similarly to in the Hubbard model. In contrast with the Hubbard model, however, the d-SC order also arises down to small δ in a wide range of t′/t (

\gtrsim

−0.2) and coexists with the AF order even for t′/t < 0 (type-II AF regime). Furthermore, there is no instability toward PS for any t′/t and δ for J/t = 0.3.