Functional renormalization for spontaneous symmetry breaking in the Hubbard model

Friederich, Simon; Krahl, Hans Christian; Wetterich, C.

doi:10.1103/physrevb.83.155125

Cited by 53 publications

(47 citation statements)

References 65 publications

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“…Interestingly, this value of doping is exactly identical to the one in the pure antiferromagnetic SDW phase discussed in last section, which suggests that the two symmetry-breaking phases are not competing so strongly at least in the present meanfield level. However, we should emphasize that if fluctuation beyond mean-field is included as shown in the typical fRG calculation [29], antiferromagnetic and superconducting order will show a tendency of mutual exclusion, which indicates a strong competition in contrast to the mean-field result. Another interesting point is that the maximal SC pairing order appears when the antiferromagnetic SDW just vanishes.…”

Section: Superconducting State With Antiferromagnetismmentioning

confidence: 94%

Coexistence of antiferromagnetism and superconductivity of t-t′-J model on honeycomb lattice

Zhong

Zhang

et al. 2015

Physica B: Condensed Matter

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a b s t r a c tMotivated by recent experimental study of antiferromagnetic property of honeycomb compound In 3 Cu 2 VO 9 [Yan et al. (2012)], we explore possible superconductivity and its coexistence with collinear antiferromagnetism. Explicitly, we use the t t J − ′ − model on the honeycomb lattice as our starting point and employ the slave-boson mean-field theory. In the antiferromagnetic normal state, the characteristic doping evolution of Fermi surface shows that only one effective singe band is active, which suggests that the potential pairing symmetry is more likely the time-reversal symmetry breaking dþid, rather than the extended s-wave pairing structure. It is found that this superconducting state coexists with the antiferromagnetism in a broad doping regime, which is consistent with the numerical calculations. The local density of states and its thermodynamic property of the superconducting state has been studied in detail with an effective single-band picture for understanding other physical observable such as superfluid density. The present work may be useful in experimentally exploring possible superconductivity of this kind of materials on the honeycomb lattice and contributes to the understanding of the unconventional superconductivity on general two-dimensional correlated electron systems.

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Section: Superconducting State With Antiferromagnetismmentioning

confidence: 94%

Coexistence of antiferromagnetism and superconductivity of t-t′-J model on honeycomb lattice

Zhong

Zhang

et al. 2015

Physica B: Condensed Matter

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“…Our method could be employed to study the pseudogap in the two dimensional Hubbard model [34][35][36][37]. Another application could be the examination of multicritical points, for which the Hubbard model provides a prominent example in the regime of competing d-wave and antiferromagnetic order [38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Machine learning of explicit order parameters: From the Ising model to SU(2) lattice gauge theory

2017

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We present a procedure for reconstructing the decision function of an artificial neural network as a simple function of the input, provided the decision function is sufficiently symmetric. In this case one can easily deduce the quantity by which the neural network classifies the input. The procedure is embedded into a pipeline of machine learning algorithms able to detect the existence of different phases of matter, to determine the position of phase transitions and to find explicit expressions of the physical quantities by which the algorithm distinguishes between phases. We assume no prior knowledge about the Hamiltonian or the order parameters except Monte Carlosampled configurations. The method is applied to the Ising Model and SU(2) lattice gauge theory. In both systems we deduce the explicit expressions of the known order parameters from the decision functions of the neural networks.

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“…In a partially bosonized formulation, exchange propagators with a quadratic frequency dependence have been used. 27,28 In various further situations RG flows with frequencydependent vertices have been studied in some detail. In the case of the single-impurity Anderson model coupled to noninteracting leads, integration over the degrees of freedom in the leads produces an effective local model in which all dependence is in the frequency variables.…”

Section: Introductionmentioning

confidence: 99%

Frequency-dependent vertex functions of the (t,t′) Hubbard model at weak coupling

2012

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We present a functional renormalization group calculation for the two-dimensional (t,t )-Hubbard model at Van Hove filling. Using a channel decomposition we describe the momentum and frequency dependence of the vertex function in the normal phase. Compared to previous studies that neglect frequency dependencies we find higher pseudocritical scales and a smaller region of d-wave superconductivity. A large contribution to the effective interaction is given by a forward-scattering process with finite frequency exchange. We test different frequency parametrizations and in a second calculation include the frequency dependence of the imaginary self-energy. We also generalize the channel decomposition to frequency-dependent fermion-boson vertex functions.

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Functional renormalization for spontaneous symmetry breaking in the Hubbard model

Cited by 53 publications

References 65 publications

Coexistence of antiferromagnetism and superconductivity of t-t′-J model on honeycomb lattice

Coexistence of antiferromagnetism and superconductivity of t-t′-J model on honeycomb lattice

Machine learning of explicit order parameters: From the Ising model to SU(2) lattice gauge theory

Frequency-dependent vertex functions of the (t,t′) Hubbard model at weak coupling

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