aqora

Tensor RG calculations and quantum simulations near criticality

Yannick Meurice, Alexei Bazavov, Shan-Wen Tsai +3 more

We discuss the reformulation of the O(2) model with a chemical potential and the Abelian Higgs model on a 1+1 dimensional space-time lattice using the Tensor Renormalization Group (TRG) method. The TRG allows exact blocking and connects smoothly the classical Lagrangian approach to the quantum Hamiltonian approach. We calculate the entanglement entropy in the superfluid phase of the O(2) model and show that it approximately obeys the logarithmic Calabrese-Cardy scaling obtained from Conformal Field Theory (CFT). We calculate the Polyakov loop in the Abelian Higgs model and discuss the possibility of a deconfinement transition at finite volume. We propose Bose-Hubbard Hamiltonians implementable on optical lattices as quantum simulators for CFT models.We discuss the reformulation of the O(2) model with a chemical potential and the Abelian Higgs model on a 1+1 dimensional space-time lattice using the Tensor Renormalization Group (TRG) method. The TRG allows exact blocking and connects smoothly the classical Lagrangian approach to the quantum Hamiltonian approach. We calculate the entanglement entropy in the superfluid phase of the O(2) model and show that it approximately obeys the logarithmic Calabrese-Cardy scaling obtained from Conformal Field Theory (CFT). We calculate the Polyakov loop in the Abelian Higgs model and discuss the possibility of a deconfinement transition at finite volume. We propose Bose-Hubbard Hamiltonians implementable on optical lattices as quantum simulators for CFT models.

arXiv:1611.08711International Symposium on Lattice Field Theory (LATTICE)Feb 18, 20177 citations

Real-Space Renormalization Group Theory

David A. Lavis, G. M. Bell

Springer eBooksJan 1, 19990 citations

Arguments towards ac-theorem from branch-point twist fields

Olalla A Castro-Alvaredo, Benjamin Doyon, Emanuele Levi

A fundamental quantity in 1+1 dimensional quantum field theories is Zamolodchikov's c-function. A function of a renormalization group distance parameter r that interpolates between UV and IR fixed points, its value is usually interpreted as a measure of the number of degrees of freedom of a model at a particular energy scale. The c-theorem establishes that c(r) is a monotonically decreasing function of r and that its derivative may only vanish at quantum critical points. At those points c(r) becomes the central charge of the conformal field theory which describes the critical point. In this letter we argue that a different function proposed by Calabrese and Cardy, defined in terms of the two-point function of a branch point twist field and the trace of the stress-energy tensor, has exactly the same qualitative features as c(r).A fundamental quantity in 1+1 dimensional quantum field theories is Zamolodchikov's c-function. A function of a renormalization group distance parameter r that interpolates between UV and IR fixed points, its value is usually interpreted as a measure of the number of degrees of freedom of a model at a particular energy scale. The c-theorem establishes that c(r) is a monotonically decreasing function of r and that its derivative may only vanish at quantum critical points. At those points c(r) becomes the central charge of the conformal field theory which describes the critical point. In this letter we argue that a different function proposed by Calabrese and Cardy, defined in terms of the two-point function of a branch point twist field and the trace of the stress-energy tensor, has exactly the same qualitative features as c(r).

arXiv:1107.4280Journal of Physics A Mathematical and TheoreticalNov 17, 201128 citations

Real-Space Renormalization Group Theory

David A. Lavis

Theoretical and mathematical physicsJan 1, 20150 citations

Scaling Theories and the Renormalization Group

Silvio R. A. Salinas

Graduate texts in contemporary physicsJan 1, 20018 citations

A new c-theorem involving branch point twist fields

Olalla A. Castro-Alvaredo, Benjamin Doyon, Emanuele Levi

A fundamental quantity in 1+1 dimensional quantum field theories is Zamolodchikov's c-function. A function of a renormalization group distance parameter r that interpolates between UV and IR fixed points, its value is usually interpreted as a measure of the number of degrees of freedom of a model at a particular energy scale. The c-theorem establishes that c(r) is a monotonically decreasing function of r and that its derivative may only vanish at quantum critical points. At those points c(r) becomes the central charge of the conformal field theory which describes the critical point. In this letter we argue that a different function proposed by Calabrese and Cardy, defined in terms of the two-point function of a branch point twist field and the trace of the stress-energy tensor, has exactly the same qualitative features as c(r).A fundamental quantity in 1+1 dimensional quantum field theories is Zamolodchikov's c-function. A function of a renormalization group distance parameter r that interpolates between UV and IR fixed points, its value is usually interpreted as a measure of the number of degrees of freedom of a model at a particular energy scale. The c-theorem establishes that c(r) is a monotonically decreasing function of r and that its derivative may only vanish at quantum critical points. At those points c(r) becomes the central charge of the conformal field theory which describes the critical point. In this letter we argue that a different function proposed by Calabrese and Cardy, defined in terms of the two-point function of a branch point twist field and the trace of the stress-energy tensor, has exactly the same qualitative features as c(r).

Jul 21, 20110 citations

Real-space renormalization group methods and the prospect of observing conformal Calabrese-Cardy scaling

Related papers

Real-space renormalization group methods and the prospect of observing conformal Calabrese-Cardy scaling

Related papers