Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1502.04739

Rényi entanglement entropy of critical SU($N$) spin chains

Jonathan D'Emidio·Matthew S. Block·Ribhu K. Kaul
View original source ↗Read source document ↗Export metadata ↓

Abstract

We present a study of the scaling behavior of the Rényi entanglement entropy (REE) in SU($N$) spin chain Hamiltonians, in which all the spins transform under the fundamental representation. These SU($N$) spin chains are known to be quantum critical and described by a well known Wess-Zumino-Witten (WZW) non-linear sigma model in the continuum limit. Numerical results from our lattice Hamiltonian are obtained using stochastic series expansion (SSE) quantum Monte Carlo for both closed and open boundary conditions. As expected for this 1D critical system, the REE shows a logarithmic dependence on the subsystem size with a prefector given by the central charge of the SU($N$) WZW model. We study in detail the sub-leading oscillatory terms in the REE under both periodic and open boundaries. Each oscillatory term is associated with a WZW field and decays as a power law with an exponent proportional to the scaling dimension of the corresponding field. We find that the use of periodic boundaries (where oscillations are less prominent) allows for a better estimate of the central charge, while using open boundaries allows for a better estimate of the scaling dimensions. For completeness we also present numerical data on the thermal Rényi entropy which equally allows for extraction of the central charge.

Explore related subjects

cond-mat.str-el

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jonathan D'Emidio, Matthew S. Block, Ribhu K. Kaul. 2015-02-16. Rényi entanglement entropy of critical SU($N$) spin chains. https://doi.org/10.1103/physrevb.92.054411

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Spontaneous Parity Breaking in Quantum Antiferromagnets on the Triangular Lattice

Frustration on the triangular lattice has long been a source of intriguing and often debated phases in many-body systems. Although symmetry analysis has been employed, the role of the seemingly trivial parity symmetry has received little attention. In this work, we show that phases induced by frustration are systematically shaped by an implicit rule-of-thumb associated with spontaneous parity breaking in weak longitudinal field. This principle enables us to anticipate and rationalize the regimes and conditions under which nontrivial phases emerge. For the spin-$S$ antiferromagnetic XXZ model, we demonstrate that a controversial parity-broken phase appears at intermediate values of $S$. In bilayer systems, enhanced frustration leads to additional phases, such as supersolids, whose properties can be classified by their characteristic parity features. Benefiting from our improved tensor network contraction techniques, we confirm these results through large-scale tensor-network calculations. This study offers an alternative viewpoint and a systematic approach for examining the interplay between spin, symmetry, and frustration in many-body systems.

cond-mat.str-el↗
arXiv2026

Directional Criticality and Higher-Order Flatness: Designing Van Hove Singularities in Three Dimensions

Van Hove singularities (VHSs) play a pivotal role in driving correlated electronic phenomena. Traditional classifications focus only on critical points where the band gradient vanishes in all directions. Here we establish a unified classification of VHSs in three-dimensional systems, characterized by the number of vanishing gradient components and Hessian eigenvalues: ordinary ($M$-type), higher-order ($T_1$, $T_2$, $T_3$), noncritical ordinary ($N_0$, $N_1$, $N_2$), and noncritical higher-order ($S_1$, $S_2$) types. Noncritical VHSs exhibit directional quenching: the gradient vanishes in a two-dimensional subspace while remaining finite along the orthogonal direction, yielding finite density-of-states enhancements with distinct energy dependencies. Using an $s$-orbital tight-binding model on the pyrochlore lattice with spin-orbit coupling, we demonstrate that all singularity classes emerge at distinct high-symmetry points through controlled tuning of the hopping ratio. This work establishes directional criticality and higher-order flatness as design principles for tailoring density-of-states enhancements in three-dimensional quantum materials.

cond-mat.str-el↗
arXiv2026

Quantum Rotors on the Fuzzy Sphere and the Cubic CFT

The three-dimensional cubic conformal field theory governs the critical behaviour of Heisenberg magnets with cubic anisotropy. Studying this theory non-perturbatively is challenging, because its most easily accessible observables are numerically very close to those of the more symmetric $O(3)$ model. In this work, we overcome this difficulty using the fuzzy sphere regularisation method. By adding a cubic-invariant two-body interaction to the quantum rotor Hamiltonian used for the $O(3)$ model, we break the continuous rotational symmetry by construction and unambiguously isolate the cubic critical point. Using exact diagonalisation and the density matrix renormalisation group, we calculate the scaling dimensions of several key operators, including the leading scalar singlets, and resolve the splitting of the $O(3)$ rank-two traceless symmetric tensor into the $E_g$ and $T_{2g}$ representations of the cubic group. Our results are consistent with existing Monte Carlo, conformal perturbation theory, and $\varepsilon$ expansion benchmarks, demonstrating the power of the fuzzy sphere in resolving closely spaced universality classes.

cond-mat.str-el↗