arXiv subjects

Erick Arguello Cruz

Publications and source records attributed to Erick Arguello Cruz.

5 recordsLinked to original sources

arXiv2026

Quantum models with the Yang-Lee phase transition

In this article, we present four different $1+1$D quantum models that realize the Yang-Lee (YL) phase transition under a deformation that preserves $PT$ symmetry. These are the antiferromagnetic Ising spin chain in transverse and longitudinal magnetic fields, the massive Schwinger model, the Blume-Capel model, and the three-state quantum clock model. Using the state-operator correspondence, we identify the YL critical point, compute the scaling dimensions of the lowest operators in each model, and find perfect agreement with the exact results for the YL criticality in two dimensions. Using bosonization for the Schwinger model and the Polyakov-Hubbard transformation for the other models, we show that in all of these quantum models the YL critical point is described, as expected, by a massless bosonic field with an $i ϕ^3$ interaction. In the quantum clock model, this critical field interacts with a massive bosonic field, and we identify the massless and massive states in the Hamiltonian spectrum. In addition, we numerically compute the two-point function of $ϕ$ at the Yang-Lee critical point and show that it grows with distance, in agreement with theoretical expectations.

hep-th↗

arXiv2026

Four-point function of the complex Sachdev-Ye-Kitaev model at finite chemical potential

It is known that, for a range of chemical potentials, the infrared behavior of the complex Sachdev-Ye-Kitaev (cSYK) model is governed by a 1D Nearly Conformal Field Theory (NCFT$_{1}$), thereby realizing a continuous line of NCFTs. A finite chemical potential $μ$ introduces an asymmetry parameter $\mathscr{E}$ into the cSYK fermion two-point function in the conformal limit. In this work, we compute the cSYK four-point function in the conformal limit for an arbitrary value of $\mathscr{E}$ at leading order in $1/N$. We show that the result is fully consistent with the NCFT$_{1}$ structure of the cSYK model and use it to extract the structure constants for correlation functions of two complex fermions with bilinear operators.

hep-th↗

arXiv2025

Yang-Lee Quantum Criticality in Various Dimensions

The Yang-Lee universality class arises when imaginary magnetic field is tuned to its critical value in the paramagnetic phase of the $d<6$ Ising model. In $d=2$, this non-unitary Conformal Field Theory (CFT) is exactly solvable via the $M(2,5)$ minimal model. As found long ago by von Gehlen using Exact Diagonalization, the corresponding real-time, quantum critical behavior arises in the periodic Ising spin chain when the imaginary longitudinal magnetic field is tuned to its critical value from below. Even though the Hamiltonian is not Hermitian, the energy levels are real due to the $PT$ symmetry. In this paper, we explore the analogous quantum critical behavior in higher dimensional non-Hermitian Hamiltonians on regularized spheres $S^{d-1}$. For $d=3$, we use the recently invented, powerful fuzzy sphere method, as well as discretization by the platonic solids cube, icosahedron and dodecaherdron. The low-lying energy levels and structure constants we find are in agreement with expectations from the conformal symmetry. The energy levels are in good quantitative agreement with the high-temperature expansions and with Padé extrapolations of the $6-ε$ expansions in Fisher's $iϕ^3$ Euclidean field theory for the Yang-Lee criticality. In the course of this work, we clarify some aspects of matching between operators in this field theory and quasiprimary fields in the $M(2,5)$ minimal model. For $d=4$, we obtain new results by replacing the $S^3$ with the self-dual polytope called the $24$-cell.

hep-th↗

arXiv2024

Precision study of the massive Schwinger model near quantum criticality

We perform a numerical analysis of the massive Schwinger model in the presence of a background electric field. Using the Density Matrix Renormalization Group (DMRG) approach, we efficiently compute the spectrum of the Schwinger model on a staggered lattice with up to 3000 qubits. As a result, we achieve a precise computation of the critical mass of the massive Schwinger model to five digits using four different 'criticality criteria', observing perfect agreement among them. Additionally, we discuss the effect of a four-fermion operator deformation of the Schwinger model and compute the critical mass for various values of the deformation parameter.

hep-th↗

arXiv2022

Precise Low-Temperature Expansions for the Sachdev-Ye-Kitaev model

We solve numerically the large $N$ Dyson-Schwinger equations for the Sachdev-Ye-Kitaev (SYK) model utilizing the Legendre polynomial decomposition and reaching $10^{-36}$ accuracy. Using this we compute the energy of the SYK model at low temperatures $T\ll J$ and obtain its series expansion up to $T^{7.54}$. While it was suggested that the expansion contains terms $T^{3.77}$ and $T^{5.68}$, we find that the first non-integer power of temperature is $T^{6.54}$, which comes from the two point function of the fermion bilinear operator $O_{h_{1}}=χ\partial_τ^{3}χ$ with scaling dimension $h_{1}\approx 3.77$. The coefficient in front of $T^{6.54}$ term agrees well with the prediction of the conformal perturbation theory. We conclude that the conformal perturbation theory appears to work even though the SYK model is not strictly conformal.

hep-th↗