Strong finite-size corrections for lattice fermions at a supersymmetric multicritical point

We study a model of spinless fermions with infinite nearest-neighbor repulsion on the square ladder, which has microscopic supersymmetry. It has been conjectured that in the continuum, the model is described by the superconformal minimal model with central charge $c=3/2$ . Thus far, it has not been possible to confirm this conjecture due to strong finite-size corrections in numerical data. We trace the origin of these corrections to the presence of unusual marginal operators that break Lorentz invariance but preserve part of the supersymmetry. By relying mostly on entanglement entropy calculations with the density-matrix renormalization group, we are able to reduce finite-size effects significantly. This allows us to unambiguously determine the continuum theory of the model. We also study perturbations of the model and establish that the supersymmetric model is a multicritical point. Our work underlines the power of entanglement entropy as a probe of the phases of quantum many-body systems.We study a model of spinless fermions with infinite nearest-neighbor repulsion on the square ladder, which has microscopic supersymmetry. It has been conjectured that in the continuum, the model is described by the superconformal minimal model with central charge $c=3/2$. Thus far, it has not been possible to confirm this conjecture due to strong finite-size corrections in numerical data. We trace the origin of these corrections to the presence of unusual marginal operators that break Lorentz invariance but preserve part of the supersymmetry. By relying mostly on entanglement entropy calculations with the density-matrix renormalization group, we are able to reduce finite-size effects significantly. This allows us to unambiguously determine the continuum theory of the model. We also study perturbations of the model and establish that the supersymmetric model is a multicritical point. Our work underlines the power of entanglement entropy as a probe of the phases of quantum many-body systems.

arXiv:1208.0343Physical Review BApr 30, 201338 citations

Criticality in one-dimensional supersymmetric lattice fermions

Matthias Troyer, Bela Bauer, Liza Huijse +2 more

Bulletin of the American Physical SocietyMar 1, 20120 citations

ひねり境界条件を使った多重臨界点付近の相転移線の計算手法

Shunji Moriya

A point where several critical lines intersect is called a multicritical point.Near such a point, multiple critical phenomena interfere and a finite-size correction becomes large.Therefore, conventional methods cannot be applied near the multicritical point.We propose a new method to numerically calculate a transition point for a quantum spin chain near the multicritical point.We treat a bond-alternating (BA) XXZ model for S = 1/2, 1, 3/2.In a ground-state phase diagram of this model, a 2D Gaussian universality transition line bifurcates into two 2D Ising universality transition lines, which make a multicritical point.At this point, Berezinskii-Kosterlitz-Thouless transition occurs, where the correlation length diverges singularly.To deal with a 2D Ising universality, we review a transverse field 1D quantum Ising (TFI) model, corresponding to the classical 2D Ising model with transfer matrix.A relation between a disorder phase and an order phase is known as the Kramers-Wannier duality transformation.We find a proper duality transformation that is exact in the finite-size TFI model with a periodic and anti-periodic boundary condition.This shows that the energies for the two boundary conditions are crossing at the transition point.A free fermion field theory is derived from the critical Ising model by taking a continuum limit.From a conformal field theory, we verify that the energy-crossing is realized in the 2D Ising universality class, not only in the TFI model.We apply our method to the BA XXZ model.The energy-crossing happens in boundary conditions that are twisted around a z-axis and y-axis.In an anisotropic limit, two energies in a finite-size are crossing at the transition point since the BA XXZ model is identical to the TFI model.on the other hand, at the multicritical point, the finite-size correction vanishes by an isotropy and a twist translation symmetry.Therefore, near the multicritical point, our method has a smaller finite-size correction.In this paper, we also review the 2D Gaussian universality.By a bosonization, the BA XXZ model can be transformed to a phase Hamiltonian composed of boson operators.The degenerate energies for a twisted boundary condition are split by a perturbation around a Gaussian fixed point.By our method, we numerically calculate a transition point of the BA XXZ model for S = 1/2, 1, 3/2.As expected, the finite-size correction of numerical results becomes very small near the multicritical point.iA point where several critical lines intersect is called a multicritical point.Near such a point, multiple critical phenomena interfere and a finite-size correction becomes large.Therefore, conventional methods cannot be applied near the multicritical point.We propose a new method to numerically calculate a transition point for a quantum spin chain near the multicritical point.We treat a bond-alternating (BA) XXZ model for S = 1/2, 1, 3/2.In a ground-state phase diagram of this model, a 2D Gaussian universality transition line bifurcates into two 2D Ising universality transition lines, which make a multicritical point.At this point, Berezinskii-Kosterlitz-Thouless transition occurs, where the correlation length diverges singularly.To deal with a 2D Ising universality, we review a transverse field 1D quantum Ising (TFI) model, corresponding to the classical 2D Ising model with transfer matrix.A relation between a disorder phase and an order phase is known as the Kramers-Wannier duality transformation.We find a proper duality transformation that is exact in the finite-size TFI model with a periodic and anti-periodic boundary condition.This shows that the energies for the two boundary conditions are crossing at the transition point.A free fermion field theory is derived from the critical Ising model by taking a continuum limit.From a conformal field theory, we verify that the energy-crossing is realized in the 2D Ising universality class, not only in the TFI model.We apply our method to the BA XXZ model.The energy-crossing happens in boundary conditions that are twisted around a z-axis and y-axis.In an anisotropic limit, two energies in a finite-size are crossing at the transition point since the BA XXZ model is identical to the TFI model.on the other hand, at the multicritical point, the finite-size correction vanishes by an isotropy and a twist translation symmetry.Therefore, near the multicritical point, our method has a smaller finite-size correction.In this paper, we also review the 2D Gaussian universality.By a bosonization, the BA XXZ model can be transformed to a phase Hamiltonian composed of boson operators.The degenerate energies for a twisted boundary condition are split by a perturbation around a Gaussian fixed point.By our method, we numerically calculate a transition point of the BA XXZ model for S = 1/2, 1, 3/2.As expected, the finite-size correction of numerical results becomes very small near the multicritical point.i

Mar 23, 20220 citations

Supersymmetry in strongly correlated fermion models

D. K. Galanakis, Stefanos Papanicolaou, Chris Henley

Bulletin of the American Physical SocietyMar 18, 20091 citation

Supersymmetry and multicriticality in a ladder of constrained fermions

Natalia Chepiga, Jiří Minář, Kareljan Schoutens

Supersymmetric lattice models of constrained fermions are known to feature exotic phenomena such as superfrustration, with an extensive degeneracy of ground states, the nature of which is however generally unknown. Here we address this issue by considering a superfrustrated model, which we deform from the supersymetric point. By numerically studying its two-parameter phase diagram, we reveal a rich phenomenology. The vicinity of the supersymmetric point features period-4 and period-5 density waves which are connected by a floating phase (incommensurate Luttinger liquid) with smoothly varying density. The supersymmetric point emerges as a multicritical point between these three phases. Inside the period-4 phase we report a valence-bond solid type ground state that persists up to the supersymmetric point. Our numerical data for transitions out of density-wave phases are consistent with the Pokrovsky-Talapov universality class. Furthermore, our analysis unveiled a period-3 phase with a boundary determined by a competition between single and two-particle instabilities accompanied by a doubling of the wavevector of the density profiles along a line in the phase diagram.Supersymmetric lattice models of constrained fermions are known to feature exotic phenomena such as superfrustration, with an extensive degeneracy of ground states, the nature of which is however generally unknown. Here we address this issue by considering a superfrustrated model, which we deform from the supersymetric point. By numerically studying its two-parameter phase diagram, we reveal a rich phenomenology. The vicinity of the supersymmetric point features period-4 and period-5 density waves which are connected by a floating phase (incommensurate Luttinger liquid) with smoothly varying density. The supersymmetric point emerges as a multicritical point between these three phases. Inside the period-4 phase we report a valence-bond solid type ground state that persists up to the supersymmetric point. Our numerical data for transitions out of density-wave phases are consistent with the Pokrovsky-Talapov universality class. Furthermore, our analysis unveiled a period-3 phase with a boundary determined by a competition between single and two-particle instabilities accompanied by a doubling of the wavevector of the density profiles along a line in the phase diagram.

arXiv:2105.04359SciPost PhysicsSep 16, 20215 citations

Correlated fermions on a lattice in high dimensions

E. M�ller-Hartmann

The European Physical Journal BDec 1, 1989650 citations

c=3/2

. Thus far, it has not been possible to confirm this conjecture due to strong finite-size corrections in numerical data. We trace the origin of these corrections to the presence of unusual marginal operators that break Lorentz invariance but preserve part of the supersymmetry. By relying mostly on entanglement entropy calculations with the density-matrix renormalization group, we are able to reduce finite-size effects significantly. This allows us to unambiguously determine the continuum theory of the model. We also study perturbations of the model and establish that the supersymmetric model is a multicritical point. Our work underlines the power of entanglement entropy as a probe of the phases of quantum many-body systems.