The crossover from weak to strong coupling for a three-dimensional continuum model of fermions interacting via an attractive contact potential is studied above the superconducting critical temperature ${T}_{c}.$ The pair-fluctuation propagator, the one-loop self-energy, and the spectral function are investigated in a systematic way from the superconducting fluctuation regime (weak coupling) to the bosonic regime (strong coupling). Analytic and numerical results are reported. In the strong-coupling regime, where the pair fluctuation propagator has bosonic character, two quite different peaks appear in the spectral function at a given wave vector, a broad one at negative frequencies and a narrow one at positive frequencies. The broad peak is asymmetric about its maximum, with its spectral weight decreasing by increasing coupling and temperature. In this regime, two crossover temperatures ${T}_{1}^{*}$ (at which the two peaks in the spectral function merge in one peak) and ${T}_{0}^{*}$ (at which the maximum of the lower peak crosses zero frequency) can be identified, with ${T}_{c}\ensuremath{\ll}{T}_{0}^{*}<{T}_{1}^{*}.$ By decreasing coupling, the two-peak structure evolves smoothly. In the weak-coupling regime, where the fluctuation propagator has diffusive Ginzburg-Landau character, the overall line shape of the spectral function is more symmetric and the two crossover temperatures approach ${T}_{c}.$ The analysis of the spectral function identifies specific features which allow one to distinguish by ARPES whether a system is in the weak- or strong-coupling regime. Connection of the results of our analysis with the phenomenology of cuprate superconductors is also attempted.The crossover from weak to strong coupling for a three-dimensional continuum model of fermions interacting via an attractive contact potential is studied above the superconducting critical temperature ${T}_{c}.$ The pair-fluctuation propagator, the one-loop self-energy, and the spectral function are investigated in a systematic way from the superconducting fluctuation regime (weak coupling) to the bosonic regime (strong coupling). Analytic and numerical results are reported. In the strong-coupling regime, where the pair fluctuation propagator has bosonic character, two quite different peaks appear in the spectral function at a given wave vector, a broad one at negative frequencies and a narrow one at positive frequencies. The broad peak is asymmetric about its maximum, with its spectral weight decreasing by increasing coupling and temperature. In this regime, two crossover temperatures ${T}_{1}^{*}$ (at which the two peaks in the spectral function merge in one peak) and ${T}_{0}^{*}$ (at which the maximum of the lower peak crosses zero frequency) can be identified, with ${T}_{c}\ensuremath{\ll}{T}_{0}^{*}<{T}_{1}^{*}.$ By decreasing coupling, the two-peak structure evolves smoothly. In the weak-coupling regime, where the fluctuation propagator has diffusive Ginzburg-Landau character, the overall line shape of the spectral function is more symmetric and the two crossover temperatures approach ${T}_{c}.$ The analysis of the spectral function identifies specific features which allow one to distinguish by ARPES whether a system is in the weak- or strong-coupling regime. Connection of the results of our analysis with the phenomenology of cuprate superconductors is also attempted.

arXiv:cond-mat/0202084Physical review. B, Condensed matterJul 3, 2002205 citations

BOSONIZATION OF THE SU (N) THIRRING MODELS

Tom Banks, D. Horn, Herbert Neuberger B

WORLD SCIENTIFIC eBooksDec 1, 19940 citations

Non-Abelian Chern-Simons theory from a Hubbard-like model

Giandomenico Palumbo, Jiannis K. Pachos

Here, we provide a simple Hubbard-like model of spin- $1/2$ fermions that gives rise to the SU(2)-symmetric Thirring model that is equivalent, in the low-energy limit, to the Yang-Mills-Chern-Simons model. First, we identify the regime that simulates the SU(2) Yang-Mills theory. Then, we suitably extend this model so that it gives rise to the SU(2) Chern-Simons theory with level $k\ensuremath{\ge}2$ that can support non-Abelian anyons. This is achieved by introducing multiple fermionic species and modifying the Thirring interactions, while preserving the SU(2) symmetry. Our proposal provides the means to theoretically and experimentally probe non-Abelian SU(2) level $k$ topological phases.Here, we provide a simple Hubbard-like model of spin-$1/2$ fermions that gives rise to the SU(2)-symmetric Thirring model that is equivalent, in the low-energy limit, to the Yang-Mills-Chern-Simons model. First, we identify the regime that simulates the SU(2) Yang-Mills theory. Then, we suitably extend this model so that it gives rise to the SU(2) Chern-Simons theory with level $k\ensuremath{\ge}2$ that can support non-Abelian anyons. This is achieved by introducing multiple fermionic species and modifying the Thirring interactions, while preserving the SU(2) symmetry. Our proposal provides the means to theoretically and experimentally probe non-Abelian SU(2) level $k$ topological phases.

arXiv:1311.2871Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsJul 14, 201417 citations

Crossovers in spin-boson and central spin models

Philip C. E. Stamp, I. S. Tupitsyn

arXiv:cond-mat/0308139Chemical PhysicsDec 17, 200318 citations

Dissipative Landau-Zener tunneling in the crossover regime from weak to strong environment coupling

Xi Dai, Robbyn Trappen, Huo Chen +22 more

Landau-Zener tunneling, which describes the transition in a two-level system during a sweep through an anti-crossing, is a model applicable to a wide range of physical phenomena. Realistic quantum systems are affected by dissipation due to coupling to their environments. An important aspect of understanding such open quantum systems is the relative energy scales of the system itself and the system-environment coupling, which distinguishes the weak- and strong-coupling regimes. Using a tunable superconducting flux qubit, we observe the crossover from weak to strong coupling to the environment in Landau-Zener tunneling. Our results confirm previous theoretical studies of dissipative Landau-Zener tunneling in the weak and strong coupling limits. We devise a spin bath model that effectively captures the crossover regime. This work is relevant for understanding the role of dissipation in quantum annealing, where the system is expected to go through a cascade of Landau-Zener transitions before reaching the target state.Landau-Zener tunneling, which describes the transition in a two-level system during a sweep through an anti-crossing, is a model applicable to a wide range of physical phenomena. Realistic quantum systems are affected by dissipation due to coupling to their environments. An important aspect of understanding such open quantum systems is the relative energy scales of the system itself and the system-environment coupling, which distinguishes the weak- and strong-coupling regimes. Using a tunable superconducting flux qubit, we observe the crossover from weak to strong coupling to the environment in Landau-Zener tunneling. Our results confirm previous theoretical studies of dissipative Landau-Zener tunneling in the weak and strong coupling limits. We devise a spin bath model that effectively captures the crossover regime. This work is relevant for understanding the role of dissipation in quantum annealing, where the system is expected to go through a cascade of Landau-Zener transitions before reaching the target state.

arXiv:2207.02017Nature CommunicationsJan 2, 20258 citations

Crossover between weak and strong coupling in 2D superconductors

M. Crişan, I. Ţifrea

Journal of Superconductivity and Novel MagnetismJun 1, 19970 citations

{T}_{c}.

The pair-fluctuation propagator, the one-loop self-energy, and the spectral function are investigated in a systematic way from the superconducting fluctuation regime (weak coupling) to the bosonic regime (strong coupling). Analytic and numerical results are reported. In the strong-coupling regime, where the pair fluctuation propagator has bosonic character, two quite different peaks appear in the spectral function at a given wave vector, a broad one at negative frequencies and a narrow one at positive frequencies. The broad peak is asymmetric about its maximum, with its spectral weight decreasing by increasing coupling and temperature. In this regime, two crossover temperatures

{T}_{1}^{*}

(at which the two peaks in the spectral function merge in one peak) and

{T}_{0}^{*}

(at which the maximum of the lower peak crosses zero frequency) can be identified, with ${T}_{c}\ensuremath{\ll}{T}_{0}^{*}<{T}_{1}^{*}.$ By decreasing coupling, the two-peak structure evolves smoothly. In the weak-coupling regime, where the fluctuation propagator has diffusive Ginzburg-Landau character, the overall line shape of the spectral function is more symmetric and the two crossover temperatures approach

{T}_{c}.

The analysis of the spectral function identifies specific features which allow one to distinguish by ARPES whether a system is in the weak- or strong-coupling regime. Connection of the results of our analysis with the phenomenology of cuprate superconductors is also attempted.

Here, we provide a simple Hubbard-like model of spin-

1/2

fermions that gives rise to the SU(2)-symmetric Thirring model that is equivalent, in the low-energy limit, to the Yang-Mills-Chern-Simons model. First, we identify the regime that simulates the SU(2) Yang-Mills theory. Then, we suitably extend this model so that it gives rise to the SU(2) Chern-Simons theory with level $k\ensuremath{\ge}2$ that can support non-Abelian anyons. This is achieved by introducing multiple fermionic species and modifying the Thirring interactions, while preserving the SU(2) symmetry. Our proposal provides the means to theoretically and experimentally probe non-Abelian SU(2) level

k

topological phases.