Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1007.2257

Understanding finite size effects in quasi-long-range orders for exactly solvable chain models

Sisi Tan·Siew Ann Cheong
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper, we investigate how much of the numerical artefacts introduced by finite system size and choice of boundary conditions can be removed by finite size scaling, for strongly-correlated systems with quasi-long-range order. Starting from the exact ground-state wave functions of hardcore bosons and spinless fermions with infinite nearest-neighbor repulsion on finite periodic chains and finite open chains, we compute the two-point, density-density, and pair-pair correlation functions, and fit these to various asymptotic power laws. Comparing the finite-periodic-chain and finite-openchain correlations with their infinite-chain counterparts, we find reasonable agreement among them for the power-law amplitudes and exponents, but poor agreement for the phase shifts. More importantly, for chain lengths on the order of 100, we find our finite-open-chain calculation overestimates some infinite-chain exponents (as did a recent density-matrix renormalization-group (DMRG) calculation on finite smooth chains), whereas our finite-periodic-chain calculation underestimates these exponents. We attribute this systematic difference to the different choice of boundary conditions. Eventually, both finite-chain exponents approach the infinite-chain limit: by a chain length of 1000 for periodic chains, and > 2000 for open chains. There is, howwever, a misleading apparent finite size scaling convergence at shorter chain lengths, for both our finite-chain exponents, as well as the finite-smooth-chain exponents. Implications of this observation are discussed.

Explore related subjects

cond-mat.str-el

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Sisi Tan, Siew Ann Cheong. 2011-04-15. Understanding finite size effects in quasi-long-range orders for exactly solvable chain models. https://doi.org/10.1016/j.physb.2011.04.035

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↗