We present a full identification of lattice model properties with their field theoretical counterparts in the continuum limit for a supersymmetric model for itinerant spinless fermions on a one-dimensional chain. The continuum limit of this model is described by an superconformal field theory (SCFT) with central charge c = 1. We identify states and operators in the lattice model with fields in the SCFT and we relate boundary conditions on the lattice to sectors in the field theory. We use the dictionary we develop in this paper to give a pedagogical explanation of a powerful tool to study supersymmetric models based on spectral flow (Huijse 2008 Phys. Rev. Lett. 101 146406). Finally, we employ the developed machinery to explain numerically observed properties of the particle density on the open chain presented in Beccaria and De Angelis (2005 Phys. Rev. Lett. 94 100401).
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.
We investigate the finite-size corrections of the entanglement entropy of critical ladders and propose a conjecture for its scaling behaviour. The conjecture is verified for free fermions, for Heisenberg ladders, and for quantum Ising ladders. Our results support that the prefactor of the logarithmic correction of the entanglement entropy of critical ladder models is universal and is associated with the central charge of the one-dimensional version of the models and with the number of branches associated with gapless excitations. Our results suggest that it is possible to infer whether there is a violation of the entropic area law in two-dimensional critical systems by analyzing the scaling behaviour of the entanglement entropy of ladder systems, which are easier to deal with.
In a
D=2+1 quantum critical system, the entanglement entropy across a boundary with a corner contains a subleading logarithmic scaling term with a universal coefficient. It has been conjectured that this coefficient is, to leading order, proportional to the number of field components
N in the associated
O(N) continuum ${\ensuremath{\phi}}^{4}$ field theory. Using density matrix renormalization group calculations combined with the powerful numerical linked cluster expansion technique, we confirm this scenario for the
O(2) Wilson-Fisher fixed point in a striking way, through direct calculation at the quantum critical points of two very different microscopic models. The value of this corner coefficient is, to within our numerical precision, twice the coefficient of the Ising fixed point. Our results add to the growing body of evidence that this universal term in the R\'enyi entanglement entropy reflects the number of low-energy degrees of freedom in a system, even for strongly interacting theories.
In this paper we study the ground-state properties of a ladder Hamiltonian with chiral
SU(2)-invariant spin interactions, a possible first step toward the construction of truly two-dimensional nontrivial systems with chiral properties starting from quasi-one-dimensional ones. Our analysis uses a recent implementation by us of
SU(2) symmetry in tensor network algorithms, specifically for infinite density matrix renormalization group. After a preliminary analysis with Kadanoff coarse graining and exact diagonalization for a small-size system, we discuss its bosonization and recap the continuum limit of the model to show that it corresponds to a conformal field theory, in agreement with our numerical findings. In particular, the scaling of the entanglement entropy as well as finite-entanglement scaling data show that the ground-state properties match those of the universality class of a
c=1 conformal field theory (CFT) in
(1+1) dimensions. We also study the algebraic decay of spin-spin and dimer-dimer correlation functions, as well as the algebraic convergence of the ground-state energy with the bond dimension, and the entanglement spectrum of half an infinite chain. Our results for the entanglement spectrum are remarkably similar to those of the spin-
21 Heisenberg chain, which we take as a strong indication that both systems are described by the same CFT at low energies, i.e., an
SU(2)1 Wess-Zumino-Witten theory. Moreover, we explain in detail how to construct matrix product operators for
SU(2)-invariant three-spin interactions, something that had not been addressed with sufficient depth in the literature.
We show that supersymmetry emerges in a large class of models in 1+1 dimensions with both Z_{2} and U(1) symmetry at the multicritical point where the Ising and Berezinskii-Kosterlitz-Thouless transitions coincide. To arrive at this result we perform a detailed renormalization group analysis of the multicritical theory including all perturbations allowed by symmetry. This analysis reveals an intricate flow with a marginally irrelevant direction that preserves part of the supersymmetry of the fixed point. The slow flow along this special line has significant consequences on the physics of the multicritical point. In particular, we show that the scaling of the U(1) gap away from the multicritical point is different from the usual Berezinskii-Kosterlitz-Thouless exponential gap scaling.