Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2501.07298

Strong Disorder Renormalization Group Method for Bond Disordered Antiferromagnetic Quantum Spin Chains with Long Range Interactions: Ground State Properties

Stefan Kettemann
View original source ↗Read source document ↗Export metadata ↓

Abstract

We introduce and implement a reformulation of the strong disorder renormalization group method in real space, well suited to study bond disordered antiferromagnetic power law coupled quantum spin chains. We derive the Master equations for the distribution function of pair distances $\tilde{r}$. First, we apply it to a short range coupled spin chain, keeping only interactions for adjacent spins. We confirm that it is solved by the infinite randomness fixed point distribution. Then, we solve the Master equation for the power law long range interaction between all spins for any anisotropy ranging from the XX-limit to the isotropic Heisenberg limit, corresponding to a tight binding chain of disordered long range interacting Fermions with long range hopping. We thereby show that the distribution function of couplings $J$ at renormalization scale $Ω$ flows to the strong disorder fixed point distribution with small corrections at $\tilde{r} > ρ,$ which depend on power exponent $α$ and coupling anisotropy $γ.$ As a consequence, the low temperature magnetic susceptibility diverges with an anomalous power law. The distribution of singlet lengths $l$ is found to decay as $l^{-2}$. The entanglement entropy of a subsystem of length $n$ increases in the ground state logarithmically for all $α$ and $γ$. After a global quantum quench the entanglement entropy increases with time logarithmically as $S(t) \sim \ln(t)/(2α)$.

Explore related subjects

cond-mat.dis-nncond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Stefan Kettemann. 2025-06-18. Strong Disorder Renormalization Group Method for Bond Disordered Antiferromagnetic Quantum Spin Chains with Long Range Interactions: Ground State Properties. https://doi.org/10.1103/b6wg-bt9k

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

KEEP EXPLORING

Related papers

arXiv2026

Sampling at intermediate temperatures is optimal for training large language models in protein structure prediction

Using a statistical mechanics framework, we investigate the parameter space of transformer models trained on protein sequence data. We sample the loss landscape at varying temperatures using Langevin dynamics to characterize the low-loss manifold, and to understand the mechanisms underlying transformers' superior performance in protein structure prediction. We find that, at variance with networks not based on the attention mechanism, the lack of a first--order--like transition in the loss of the transformer produces a range of intermediate temperatures with good learning properties; this is true both for synthetic and natural protein sequences. We also show that the parameters of most layers are highly conserved at these temperatures if the dimension of the embedding is optimal, and we provide an operative way to find this dimension. Additionally, we show that the attention matrix is more predictive of the contact maps of the protein at higher temperatures and for higher dimensions of the embedding than those optimal for learning. Finally, we showed that the models sampled at intermediate temperatures can predict the free-energy variation upon mutation, better than models obtained through standard optimization techniques.

cond-mat.dis-nn↗
arXiv2026

The Cross-Substrate Access Assay: What an Indicator Test Must Declare to Travel from Brain to Language Model

Testing an artificial system for a property linked to consciousness means applying a measurement developed on brains to a system that is not one. Such a transfer must re-examine five parts of the procedure: the competing statistical models, how they are fitted, the unit the inference generalizes over, the quantity the uncertainty interval is about, and the rule that turns a result into a verdict. The Cross-Substrate Access Assay declares all five. Because brain and model signals share no physical scale, every model is scored by the cross-entropy it assigns to held-out data, in nats per trial. The test case is the global neuronal workspace theory, which predicts that near threshold a stimulus either enters a capacity-limited workspace or does not, so that single-trial responses form a mixture of two states. A published test of this prediction on twenty people's electroencephalograms partly reproduces in a re-implementation: the first crossing and the broad ordering over time match, the window-by-window agreement does not. On 12,000 synthetic datasets generated with a single graded state, all of them members of the families the procedure fits and none within 0.0067 nat per trial of the decision boundary, the two models of that test carried over unchanged reported two states in 989 and the expanded families in none; on 600 datasets carrying a mixture the expanded procedure reported two states in 599. Its nominal 95% interval contained the procedure's mean result less often than the required 90% at six of twelve graded settings. No claim about experience is made.

cond-mat.dis-nn↗
arXiv2026

Measure-zero delocalization in the complex plane: exact mobility arcs in a non-Hermitian off-diagonal quasiperiodic lattice

We investigate Anderson localization in a one-dimensional lattice with non-Hermitian off-diagonal quasiperiodic disorder, extending a recently studied Hermitian mosaic model to the non-Hermitian regime. Using Avila's global theory, we derive the exact Lyapunov exponent and the complete phase diagram in the complex energy plane. This work contains two central findings. First, we discover mobility arcs---open curved segments in the complex plane---as a new class of mobility edges and the generic form of open mobility edges, which coexist with closed mobility rings in a complementary parameter regime. These arcs share the same localization physics as the previously reported mobility lines: eigenstates are delocalized if and only if their energies lie exactly on these sets; any deviation yields localized states. This constitutes a striking measure-zero delocalization phenomenon: delocalized states occupy only zero-measure sets (arcs or lines) in the complex plane, in sharp contrast to the mobility rings, which enclose a finite-area region of delocalized states. Second, we reveal that mobility rings, arcs, and lines all share a common mathematical origin in the generalized Joukowski transformation $P(E) = \frac{1}{2}(u - w^2/u)$, rooted in the algebraic structure of the underlying polynomial: the preimage of the boundary of an elliptical region under the polynomial map $P(E)$ gives the rings, while the branch cut inside this ellipse gives rise to the mobility arcs and lines in the complementary parameter regime.

cond-mat.dis-nn↗