Statistical Field Theory

We study the free fermion theory in 1+1 dimensions deformed by chemical potentials for holomorphic, conserved currents at finite temperature and on a spatial circle. For a spin-three chemical potential µ, the deformation is related at high temperatures to a higher spin black hole in hs[0] theory on AdS 3 spacetime. We calculate the order µ 2 corrections to the single interval Rényi and entanglement entropies on the torus using the bosonized formulation. A consistent result, satisfying all checks, emerges upon carefully accounting for both perturbative and winding mode contributions in the bosonized language. The order µ 2 corrections involve integrals that are finite but potentially sensitive to contact term singularities. We propose and apply a prescription for defining such integrals which matches the Hamiltonian picture and passes several non-trivial checks for both thermal corrections and the Rényi entropies at this order. The thermal corrections are given by a weight six quasi-modular form, whilst the Rényi entropies are controlled by quasi-elliptic functions of the interval length with modular weight six. We also point out the well known connection between the perturbative expansion of the partition function in powers of the spin-three chemical potential and the Gross-Taylor genus expansion of large-N Yang-Mills theory on the torus. We note the absence of winding mode contributions in this connection, which suggests qualitatively different entanglement entropies for the two systems.

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“…[11,55]). In particular this implies that the correlator of the holomorphic current ∂ϕ, up to an additive constant, is…”

Section: Jhep04(2015)041mentioning

confidence: 99%

Conformal perturbation theory and higher spin entanglement entropy on the torus

Datta

David

Kumar

2015

J. High Energ. Phys.

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“…(1) Here, c (c † ) denote creation (annihilation) operators for electrons, n l,σ ≡ c † l,σ c l,σ , n l ≡ n l,↑ + n l,↓ , t 0 is the hopping integral between nearest neighbors, U and V are on-site and nearest-neighbor potentials, respectively. An infinite system of noninteracting electrons possesses a divergent density of states at the Fermi level, and this plays a key role for the occurrence of various types of ordering specific for the physics in one dimension: Peierls dimerization, CDW, SDW, etc.…”

Section: Modelmentioning

confidence: 99%

“…Three well-established types of orderings that are possible in model (1) can easily be understood by examining the (classical) limit t 0 → 0. Then, for V > 0 and U < 2V , the lowest energy corresponds to doubly occupied sites and unoccupied sites alternating periodically (the bipolaronic limit of a CDW).…”

Section: Types Of Ground States Of Finite Ringsmentioning

confidence: 99%

“…The finite hopping yields a certain difference between the weights (w) in the ground states |s ± of the various Actually, there is a more general reason why a perfect antiferromagnetic ordering can never be reached within the model (1). Straightforward calculations show that, unlike |CDW ± and |CS ± , the states |SDW ± are not eigenstates of the total spin operator S. Since [S 2 , H] = 0, |s ± are exact eigenstates of both operators H and S. Therefore, whatever the parameter values (in particular, even for U/t 0 2V/t 0 1), the expansions of |s ± always contain nonvanishing contributions from multielectronic configurations different from |SDW ± .…”

Section: Correlation Functions and Optical Propertiesmentioning

confidence: 99%

“…Exact or almost exact numerical methods (exact diagonalization, Monte Carlo, density matrix renormalization group) [1] are extensively used to study models for strongly correlated systems that cannot be solved analytically. Usually, such numerical studies are ultimately devoted to infinite systems.…”

Section: Introductionmentioning

confidence: 99%

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Collective quantum tunneling of strongly correlated electrons in commensurate mesoscopic rings

2001

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We present a new effect that is possible for strongly correlated electrons in commensurate mesoscopic rings: the collective tunneling of electrons between classically equivalent configurations, corresponding to ordered states possessing charge and spin density waves (CDW, SDW) and charge separation (CS). Within an extended Hubbard model at half filling studied by exact numerical diagonalization, we demonstrate that the ground state phase diagram comprises, besides conventional critical lines separating states characterized by different orderings (e.g. CDW, SDW, CS), critical lines separating phases with the same ordering (e.g. CDW-CDW) but with different symmetries. While the former also exist in infinite systems, the latter are specific for mesoscopic systems and directly related to a collective tunnel effect. We emphasize that, in order to construct correctly a phase diagram for mesoscopic rings, the examination of CDW, SDW and CS correlation functions alone is not sufficient, and one should also consider the symmetry of the wave function that cannot be broken. We present examples demonstrating that the jumps in relevant physical properties at the conventional and new critical lines are of comparable magnitude. These transitions could be studied experimentally e.g. by optical absorption in mesoscopic systems. Possible candidates are cyclic molecules and ring-like nanostructures of quantum dots. PACS. 71.45.Lr Charge-density-wave systems -75.30.Fv Spin-density waves -72.15.Nj Collective modes (e.g., in one-dimensional conductors -73.20.Mf Collective excitations (including excitons, polarons, plasmons and other charge-density excitations)

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Tails of the density of states of two-dimensional Dirac fermions

Villain-Guillot

Jug

Ziegler³

2000

Ann. Phys.

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The density of states of Dirac fermions with a random mass on a two-dimensional lattice is considered. We give the explicit asymptotic form of the single-electron density of states as a function of both energy and (average) Dirac mass, in the regime where all states are localized. We make use of a weak-disorder expansion in the parameter g/m 2 , where g is the strength of disorder and m the average Dirac mass for the case in which the evaluation of the (supersymmetric) integrals corresponds to non-uniform solutions of the saddle point equation. The resulting density of states has tails which deviate from the typical pure Gaussian form by an analytic prefactor.

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Statistical Field Theory

Cited by 670 publications

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Conformal perturbation theory and higher spin entanglement entropy on the torus

Conformal perturbation theory and higher spin entanglement entropy on the torus

Collective quantum tunneling of strongly correlated electrons in commensurate mesoscopic rings

Tails of the density of states of two-dimensional Dirac fermions

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