Introduction to the Statistical Physics of Integrable Many-body Systems

Šamaj, L.; Bajnok, Zoltán

doi:10.1017/cbo9781139343480

Cited by 109 publications

(147 citation statements)

References 16 publications

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“…In a super Fermi liquid, the perturbing operators O's are integer fields (specifically and technically, Kac Moody descendants of the identity operator [9], specifically and physically, fields built out of the fermion fields Ψ a and Ψ † a ). It results that nested commutators of H (24) so that the whole Keldysh expansion can be formally resumed (see Fig.4) by defining the effective operators:…”

Section: Around the Sc Fixed Point Computation Detailsmentioning

confidence: 99%

“…The determination ofÎ Kac Moody descendent fields [9] of the identity operator with conformal weights ≤ n + 1, and all one needs to known is how to actually evaluate (25), or equivalently, using (24), the coefficient in (z − w) −1 in the OPE O(z)Φ(w) = n {O Φ} n (w) (z−w) n for an arbitrary field Φ in E n . This can be done recursively by using the elementary OPE Ψ † a (z)Ψ b (w) = δ ab 2π(z−w) + regular.…”

Section: Around the Sc Fixed Point Computation Detailsmentioning

confidence: 99%

“…Exact results, beside their fundamental interest, would therefore be a precious tool to assess the validity of more general, approximate methods. Since many QIM are integrable [24] (and thus exactly solvable) at equilibrium, one could hope for a full exact solution out-of-equilibrium. While this is in fact the case for free (i.e.…”

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confidence: 99%

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Out-of-Equilibrium Properties and Nonlinear Effects for Interacting Quantum Impurity Systems in the Strong-Coupling Regime

Freton

Boulat²

2014

Phys. Rev. Lett.

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We provide an exact description of out-of-equilibrium fixed points in quantum impurity models, that is able to treat time-dependent forcing. Building on this, we then show that analytical out-ofequilibrium results, that exactly treat interactions, can be obtained in interacting quantum impurity models in their strong coupling regime, provided they are integrable at equilibrium and they are "super Fermi liquids", i.e. they only allow for integer charge hopping. For such systems we build an out-of-equilibrium strong coupling expansion, akin to a Sommerfeld expansion in interacting systems. We apply our approach to the Interacting Resonant Level model, and obtain the exact expansion around the low energy fixed point of the universal scaling function for the charge current as a function of voltage, temperature, and frequency, up to order seven.The study of nano structures forced out-of-equilibrium is a vivid field of research, driven amongst other things by long term efforts towards the miniaturization of electronics. Rapid progresses in the realization of engineered micrometric structures coupled to macroscopic electrodes (e.g. quantum dots [1, 2]), or of hybrid devices consisting of atoms or molecules embedded in circuits [3][4][5] demonstrate the possibility of "single electron" electronics [6, 7]. A theoretical understanding of the mechanisms governing transport in those systems is thus of crucial importance. Whereas linear response -when the voltage across the nanostructure goes to zero -boils down to equilibrium properties and is fairly well understood, nonlinear effects are significantly harder to predict: solving the out-of-equilibrium theory unfortunately turns out to be a considerable problem, mixing many-body aspects (interactions make it complicated) with the intrinsically open geometry of the out-of-equilibrium problem.Those systems are modeled by quantum impurity models (QIM), that consist in continua of electronic degrees of freedom representing the metallic electrodes (the baths) interacting with the nanostructure (the "impurity"). A generic feature of QIM at equilibrium is that the impurity/bath coupling, no matter how small, has drastic consequence on the groundstate of the system: impurity degrees of freedom hybridize with the bath, so that effectively some, or all, impurity degrees of freedom are swallowed by the baths. In the zero energy E → 0 (groundstate) limit, impurity degrees of freedom are strongly bound to the baths, so that is is often called a strong coupling (SC) fixed point (FP). This last term means that the system has scale invariance in this limit [8, 9], resulting in the fact that the SC-FP is essentially an homogenous (the impurity "disappears") and free theory. This has direct physical consequences: for example, for systems with a Fermi liquid SC-FP [10,11], hybridization results in a linear I(V ) characteristic at small voltage, with the conductivity G 0 = ∂I ∂V V=0being maximal at T = 0 and at the particle-hole symmetric point. A typical energy scale, called here the hybridiza...

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Section: Around the Sc Fixed Point Computation Detailsmentioning

confidence: 99%

Section: Around the Sc Fixed Point Computation Detailsmentioning

confidence: 99%

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Out-of-Equilibrium Properties and Nonlinear Effects for Interacting Quantum Impurity Systems in the Strong-Coupling Regime

Freton

Boulat²

2014

Phys. Rev. Lett.

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“…Each lattice side carries the (n 2 − 1)-dimensional, adjoint representation of su(n). Since the R-matrix (20) satisfies R(0) = σ, the integrable Hamiltonian is given by [3] …”

Section: Integrable Su(n) Spin Chainsmentioning

confidence: 99%

“…An R-matrix R(λ) : V ⊗ V → V ⊗ V for λ ∈ C is a solution of the Yang-Baxter equation R 12 (λ) R 13 (λ + µ) R 23 (µ) = R 23 (µ) R 13 (λ + µ) R 12 (λ) (1) on the tensor product V ⊗ V ⊗ V , where R ij (λ) acts non-trivially on the i-th and j-th factor, eg, R 12 (λ) = R(λ) ⊗ 1. Solutions of the Yang-Baxter equation play a central role in various fields of theoretical physics like the quantum inverse scattering method [1], statistical field theories with factorised scattering [2,3], the theory of quantum groups [4,5], or quantum information theory [6,7]. In the early 1980s many rational R-matrices beyond the simplest case of the fundamental representation of su (2) have been constructed, see, eg, Refs.…”

Section: Introductionmentioning

confidence: 99%