We apply the flow equation method for studying the fermion systems where pairing interactions can either trigger the BCS instability with the symmetry breaking manifested by the off-diagonal order parameter or lead to the gaped single particle spectrum without any symmetry breaking. We construct the continuous Bogoliubov transformation in a scheme resembling the renormalization group procedure. We further extend this continuous transformation to a case where fermion pairs interact with the boson field. Due to temporal quantum fluctuations the single particle excitation spectrum develops a gap which is centered around the renormalized boson energy. When bosons undergo the Bose Einstein condensation this structure evolves into the BCS spectrum.We apply the flow equation method for studying the fermion systems where pairing interactions can either trigger the BCS instability with the symmetry breaking manifested by the off-diagonal order parameter or lead to the gaped single particle spectrum without any symmetry breaking. We construct the continuous Bogoliubov transformation in a scheme resembling the renormalization group procedure. We further extend this continuous transformation to a case where fermion pairs interact with the boson field. Due to temporal quantum fluctuations the single particle excitation spectrum develops a gap which is centered around the renormalized boson energy. When bosons undergo the Bose Einstein condensation this structure evolves into the BCS spectrum.

arXiv:cond-mat/0602236Feb 9, 20060 citations

Thermodynamics of the BCS model through large deviations

Nick G. Duffield, J. V. Pul�

Letters in Mathematical PhysicsNov 1, 19878 citations

Interplay of topology and interaction in an exactly solvable SSH-BCS-Hubbard chain

Yuejiu Zhao, Jian-Jian Miao, Fu‐Chun Zhang

We propose an SSH-BCS-Hubbard chain model and theoretically study the interplay of topology and interaction therein. We obtain the exact solution of the model at the symmetric point. The exact solution reveals that the Hubbard interaction induces ${Z}_{2}$ symmetry breaking, which leads to the coexistence and competition of antiferromagnetic order and $\ensuremath{\eta}$-pairing order. The interaction splits the zero-energy states into in-gap states and destroys the symmetry-protected topological state of the SSH-BCS chain. However, the symmetry analysis reveals that the interacting topological state can exist for small Hubbard interaction and dimerization. The topological phase transition of the perturbed SSH-BCS-Hubbard is studied via the spectral ${Z}_{2}$ topological invariant. Our study uncovers a stable interacting topological state coexisting with symmetry-breaking induced intertwined orders.We propose an SSH-BCS-Hubbard chain model and theoretically study the interplay of topology and interaction therein. We obtain the exact solution of the model at the symmetric point. The exact solution reveals that the Hubbard interaction induces ${Z}_{2}$ symmetry breaking, which leads to the coexistence and competition of antiferromagnetic order and $\ensuremath{\eta}$-pairing order. The interaction splits the zero-energy states into in-gap states and destroys the symmetry-protected topological state of the SSH-BCS chain. However, the symmetry analysis reveals that the interacting topological state can exist for small Hubbard interaction and dimerization. The topological phase transition of the perturbed SSH-BCS-Hubbard is studied via the spectral ${Z}_{2}$ topological invariant. Our study uncovers a stable interacting topological state coexisting with symmetry-breaking induced intertwined orders.

Physical review. B./Physical review. BDec 2, 20242 citations

A generalized fluctuation-dissipation theorem

Á. Stáhl, Richard Bausch, H. K. Janssen

Physics Letters AJan 1, 19673 citations

Fluctuations and Symmetry

Yu. A. Izyumov, V. N. Syromyatnikov

Springer eBooksJan 1, 19900 citations

Competition of Fermi surface symmetry breaking and superconductivity

Hiroyuki Yamase, Walter Metzner

We analyze a mean-field model of electrons on a square lattice with two types of interaction: forward scattering favoring a $d$ -wave Pomeranchuk instability and a BCS pairing interaction driving $d$ -wave superconductivity. By tuning the interaction parameters a rich variety of phase diagrams is obtained. If the BCS interaction is not too strong, Fermi surface symmetry breaking is stabilized around van Hove filling, and coexists with superconductivity at low temperatures. For pure forward scattering Fermi surface symmetry breaking occurs typically via a first order transition at low temperatures. The presence of superconductivity reduces the first order character of this transition and, if strong enough, can turn it into a continuous one. This gives rise to a quantum critical point within the superconducting phase. The superconducting gap tends to suppress Fermi surface symmetry breaking. For a relatively strong BCS interaction, Fermi surface symmetry breaking can be limited to intermediate temperatures, or can be suppressed completely by pairing.We analyze a mean-field model of electrons on a square lattice with two types of interaction: forward scattering favoring a $d$-wave Pomeranchuk instability and a BCS pairing interaction driving $d$-wave superconductivity. By tuning the interaction parameters a rich variety of phase diagrams is obtained. If the BCS interaction is not too strong, Fermi surface symmetry breaking is stabilized around van Hove filling, and coexists with superconductivity at low temperatures. For pure forward scattering Fermi surface symmetry breaking occurs typically via a first order transition at low temperatures. The presence of superconductivity reduces the first order character of this transition and, if strong enough, can turn it into a continuous one. This gives rise to a quantum critical point within the superconducting phase. The superconducting gap tends to suppress Fermi surface symmetry breaking. For a relatively strong BCS interaction, Fermi surface symmetry breaking can be limited to intermediate temperatures, or can be suppressed completely by pairing.

arXiv:cond-mat/0701660Physical Review BApr 25, 200755 citations

{Z}_{2}

symmetry breaking, which leads to the coexistence and competition of antiferromagnetic order and $\ensuremath{\eta}$-pairing order. The interaction splits the zero-energy states into in-gap states and destroys the symmetry-protected topological state of the SSH-BCS chain. However, the symmetry analysis reveals that the interacting topological state can exist for small Hubbard interaction and dimerization. The topological phase transition of the perturbed SSH-BCS-Hubbard is studied via the spectral

{Z}_{2}

topological invariant. Our study uncovers a stable interacting topological state coexisting with symmetry-breaking induced intertwined orders.

We analyze a mean-field model of electrons on a square lattice with two types of interaction: forward scattering favoring a

d

-wave Pomeranchuk instability and a BCS pairing interaction driving

d

-wave superconductivity. By tuning the interaction parameters a rich variety of phase diagrams is obtained. If the BCS interaction is not too strong, Fermi surface symmetry breaking is stabilized around van Hove filling, and coexists with superconductivity at low temperatures. For pure forward scattering Fermi surface symmetry breaking occurs typically via a first order transition at low temperatures. The presence of superconductivity reduces the first order character of this transition and, if strong enough, can turn it into a continuous one. This gives rise to a quantum critical point within the superconducting phase. The superconducting gap tends to suppress Fermi surface symmetry breaking. For a relatively strong BCS interaction, Fermi surface symmetry breaking can be limited to intermediate temperatures, or can be suppressed completely by pairing.