Spectrum of the Wilson-Fisher conformal field theory on the torus

Whitsitt, Seth; Schuler, Michael; Henry, Louis-Paul; Läuchli, Andreas M.; Sachdev, Subir

doi:10.1103/physrevb.96.035142

Cited by 19 publications

(32 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The estimated values are about twice the extrapolated values, perhaps indicating non-negligible nonpertubative corrections to ∆ Q for smaller N . However, the conclusion that monopole operators with Q = 1, 2, 3 are relevant (∆ Q < 3) at O(2) fixed point still remains true.FINITE-SIZE SPECTRUMRecently, the universal features in the finite-size critical spectrum of operators have been of interest[31][32][33]. Here, we provide a computation of critical spectrum of Dirac monopole at the O(2) fixed point of XY model.…”

mentioning

confidence: 99%

Monopole scaling dimension using Monte-Carlo simulation

Karthik

2018

Phys. Rev. D

View full text Add to dashboard Cite

We present a viable Monte Carlo determination of the scaling dimensions ∆ Q of flux Q Abelian monopoles through finite-size scaling analysis of the free energy to introduce the background field of classical Dirac monopole-antimonopole pair at critical points of three-dimensional lattice theories. We validate the method in free fermion theory, and by verifying the particle-vortex duality between the monopole scaling dimension at the inverse-XY fixed point and the charge scaling dimension at the XY fixed point. At the O(2) Wilson-Fisher fixed point, we determine the critical exponents ∆ 1 = 0.13(2), ∆ 2 = 0.29(1) and ∆ 3 = 0.47(2), which we find to be proportional to the finite-size critical spectrum of monopoles on square torus. arXiv:1808.08970v1 [cond-mat.str-el]

show abstract

mentioning

confidence: 99%

Monopole scaling dimension using Monte-Carlo simulation

Karthik

2018

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…While the universal description of a critical point is a property of 1D systems (the nature of conformal critical points in 2D is an open question and a subject of cutting-edge numerical studies [10,11]), it has been proposed that critical 1D systems can serve as building blocks of 2D topologically ordered states of matter [12][13][14][15]. Critical 1D systems can be arranged into 2D array and when coupled together in a designed fashion, the system can become a gapped topologically ordered state whose nature depends only on the couplings and on the CFT describing the critical 1D systems.…”

Section: Introductionmentioning

confidence: 99%

Quantum criticality in many-body parafermion chains

2021

View full text Add to dashboard Cite

We construct local generalizations of 3-state Potts models with exotic critical points. We analytically show that these are described by non-diagonal modular invariant partition functions of products of Z_3Z3 parafermion or u(1)_6u(1)6 conformal field theories (CFTs). These correspond either to non-trivial permutation invariants or block diagonal invariants, that one can understand in terms of anyon condensation. In terms of lattice parafermion operators, the constructed models correspond to parafermion chains with many-body terms. Our construction is based on how the partition function of a CFT depends on symmetry sectors and boundary conditions. This enables to write the partition function corresponding to one modular invariant as a linear combination of another over different sectors and boundary conditions, which translates to a general recipe how to write down a microscopic model, tuned to criticality. We show that the scheme can also be extended to construct critical generalizations of kk-state clock type models.

show abstract

“…In fact, another way to identify and chart universality classes is to measure their critical torus energy spectrum as it was shown in Refs. [13][14][15][16] for Wilson-Fisher and topological phase transitions. The low-energy gaps at a relativistic critical point on the torus are given, up to a non-universal factor v describing the effective speed of light, by universal numbers ξ i times 1/L, where L is the linear extent of the cluster [17].…”

Section: Introductionmentioning

confidence: 99%

Torus Spectroscopy of the Gross-Neveu-Yukawa Quantum Field Theory: Free Dirac versus Chiral Ising Fixed Point

Schuler,

Hesselmann,

Whitsitt

et al. 2019

Preprint

Self Cite

View full text Add to dashboard Cite

We establish the universal torus low-energy spectra at the free Dirac fixed point and at the strongly coupled chiral Ising fixed point and their subtle crossover behaviour in the Gross-Neuveu-Yukawa field theory with nD = 4 component Dirac spinors in D = (2 + 1) dimensions. These fixed points and the field theories are directly relevant for the long-wavelength physics of certain interacting Dirac systems, such as repulsive spinless fermions on the honeycomb lattice or π-flux square lattice. The torus spectrum has been shown previously to serve as a characteristic fingerprint of relativistic fixed points and is a powerful tool to discriminate quantum critical behaviour in numerical simulations. Here we use a combination of exact diagonalization and quantum Monte Carlo simulations of strongly interacting fermionic lattice models, to compute the critical energy spectrum on finite-size clusters with periodic boundaries and extrapolate them to the thermodynamic limit. Additionally, we compute the torus spectrum analytically using the perturbative expansion in = 4 − D, which is in good agreement with the numerical results, thereby validating the presence of the chiral Ising fixed point in the lattice models at hand. We show that the strong interaction between the spinor field and the scalar orderparameter field strongly influences the critical torus spectrum. Building on these results we are able to address the subtle crossover physics of the low-energy spectrum flowing from the chiral Ising fixed point to the Dirac fixed point, and analyze earlier flawed attempts to extract Fermi velocity renormalizations from the low-energy spectrum.

show abstract

Spectrum of the Wilson-Fisher conformal field theory on the torus

Cited by 19 publications

References 51 publications

Monopole scaling dimension using Monte-Carlo simulation

Monopole scaling dimension using Monte-Carlo simulation

Quantum criticality in many-body parafermion chains

Torus Spectroscopy of the Gross-Neveu-Yukawa Quantum Field Theory: Free Dirac versus Chiral Ising Fixed Point

Contact Info

Product

Resources

About