Correlation versus Causation in Quantum Criticality

• URL: http://arxiv.org/abs/2608.12770v1
• Date: Thu, 13 Aug 2026 03:27:28 GMT
• Title: Correlation versus Causation in Quantum Criticality
• Abstract summary: Correlation functions $langle O_1(x) O(0) rangle$ reveal scaling dimensions through spatial decay.<n>In higher-dimensional CFTs, this mechanism ensures leading causation arises from primaries.<n>We explain anomalously small edge-mode splittings and guiding our construction of spin chains with splittings as small as $1/L18$ and $1/L25$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Correlation functions $\langle O_1(x) O_2(0) \rangle$ reveal scaling dimensions through spatial decay. We instead consider static susceptibility, the change in $\langle O_1(x) \rangle$ from perturbing the Hamiltonian by $O_2(0)$, which we term causation for short. In a conformal field theory (CFT), dimensional analysis predicts decay of $|x|^{-2Δ}$ for correlation and $|x|^{-2Δ+1}$ for causation. Yet we find causation can decay up to fifteen additional orders in $x$ through a general mechanism, which we trace to time-derivative fields being unable to contribute to static response. In higher-dimensional CFTs, this mechanism ensures leading causation arises from primaries, even when descendants dominate correlation, which we leverage with DMRG to identify a previously unresolved corner primary of $Δ\approx 8.8$ and a heavy magnetic line defect primary of $Δ\approx 4.6$ in the $(2+1)$D critical Ising model. Moreover, the same mechanism governs edge-mode localization in $(1+1)$D gapless symmetry-protected topological phases, explaining previously observed anomalously small edge-mode splittings and guiding our construction of spin chains with splittings as small as $1/L^{18}$ and $1/L^{25}$.

Related papers

• Partially Correlated Verifier Cascades in LLM Harnesses: Concave Log-Odds, Polynomial Reliability, and Blind-Spot Ceilings [0.5076419064097734]
  Serial verification gates are a core reliability primitive in LLM harnesses.<n>A candidate answer is returned only if $k$ verifier calls all accept it.<n>This note gives a minimal such theory.
  arXiv  Detail & Related papers  (2026-07-15T14:58:37Z)
• When Does $\ell_2$-Boosting Overfit Benignly? High-Dimensional Risk Asymptotics and the $\ell_1$ Implicit Bias [15.113649527486276]
  We show that benign overfitting fails at the linear rate.<n>We show that while this localization mechanism should persist in the presence of signals, the exact signal-noise decomposition remains an open problem.
  arXiv  Detail & Related papers  (2026-05-07T14:14:09Z)
• Tight Bounds for Logistic Regression with Large Stepsize Gradient Descent in Low Dimension [36.3266119975955]
  We consider the optimization problem of minimizing the logistic gradient with descent to train a linear model for binary classification with separable data.<n>We show that GD with a sufficiently large learning rate $$ finds a point with loss smaller than $mathcalO (1/(T))$, as long as $T geq (n/+ 1/2)$, where $n$ is the dataset size.
  arXiv  Detail & Related papers  (2026-02-12T22:58:18Z)
• Real-time Scattering in φ^4 Theory using Matrix Product States [0.0]
  We investigate the critical behavior and real-time scattering dynamics of the interacting $4$ quantum field theory in $(1+1)$ dimensions.<n>A finite-entanglement scaling analysis at $= 0.8$ bounds the critical mass-squared to $_c2 in [-0.3190,-0.3185]$ and provides a quantitative map of the symmetric, near-critical, weakly broken, and deeply broken regimes.
  arXiv  Detail & Related papers  (2025-11-19T18:55:00Z)
• Theta-term in Russian Doll Model: phase structure, quantum metric and BPS multifractality [45.88028371034407]
  We investigate the phase structure of the deterministic and disordered versions of the Russian Doll Model (RDM)<n>We find the pattern of phase transitions in the global charge $Q(theta,gamma)$, which arises from the BA equation.<n>We conjecture that the Hamiltonian of the RDM model describes the mixing in particular 2d-4d BPS sector of the Hilbert space.
  arXiv  Detail & Related papers  (2025-10-23T17:25:01Z)
• Mesoscopic Fluctuations and Multifractality at and across Measurement-Induced Phase Transition [46.176861415532095]
  We explore statistical fluctuations over the ensemble of quantum trajectories in a model of two-dimensional free fermions.<n>Our results exhibit a remarkable analogy to Anderson localization, with $G_AB$ corresponding to two-terminal conductance.<n>Our findings lay the groundwork for mesoscopic theory of monitored systems, paving the way for various extensions.
  arXiv  Detail & Related papers  (2025-07-15T13:44:14Z)
• Out-of-equilibrium dynamics across the first-order quantum transitions of one-dimensional quantum Ising models [0.0]
  We study the out-of-equilibrium dynamics of one-dimensional quantum Ising models in a transverse field $g$.<n>We consider nearest-neighbor Ising chains of size $L$ with periodic boundary conditions.
  arXiv  Detail & Related papers  (2025-04-14T20:00:27Z)
• Convergence Rate Analysis of LION [54.28350823319057]
  LION converges iterations of $cal(sqrtdK-)$ measured by gradient Karush-Kuhn-T (sqrtdK-)$. We show that LION can achieve lower loss and higher performance compared to standard SGD.
  arXiv  Detail & Related papers  (2024-11-12T11:30:53Z)
• Correlated volumes for extended wavefunctions on a random-regular graph [0.0]
  We analyze the ergodic properties of a metallic wavefunction for the Anderson model in a disordered random-regular graph with branching number $k=2. We extract their corresponding fractal dimensions $D_q$ in the thermodynamic limit together with correlated volumes $N_q$ that control finite-size effects.
  arXiv  Detail & Related papers  (2023-11-13T19:15:18Z)
• Measurement-induced phase transition for free fermions above one dimension [46.176861415532095]
  Theory of the measurement-induced entanglement phase transition for free-fermion models in $d>1$ dimensions is developed. Critical point separates a gapless phase with $elld-1 ln ell$ scaling of the second cumulant of the particle number and of the entanglement entropy.
  arXiv  Detail & Related papers  (2023-09-21T18:11:04Z)
• Causal Bandits for Linear Structural Equation Models [58.2875460517691]
  This paper studies the problem of designing an optimal sequence of interventions in a causal graphical model. It is assumed that the graph's structure is known and has $N$ nodes. Two algorithms are proposed for the frequentist (UCB-based) and Bayesian settings.
  arXiv  Detail & Related papers  (2022-08-26T16:21:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.