A c-theorem for the effective central charge in the R=1 replica limit, and applications to systems with measurement-induced randomness

• URL: http://arxiv.org/abs/2507.07959v1
• Date: Thu, 10 Jul 2025 17:41:31 GMT
• Title: A c-theorem for the effective central charge in the R=1 replica limit, and applications to systems with measurement-induced randomness
• Authors: Rushikesh A. Patil, Andreas W. W. Ludwig,
• Abstract summary: We show that the infrared value of $c_texteff$ is always $textitless$ than the central charge $c$ of the unperturbed CFT $S_*$.<n>We consider replica field theories in the limit of $R to 1$ replicas of the form above, shown by Nahum and Jacobsen.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a general theorem demonstrating non-perturbatively the decrease of the "effective central charge" $c_{\text{eff}}=(d c/dR)|_{R=1}$ under renormalization group (RG) flow in the $R\rightarrow1$ replica limit of a $R$-copy $2D$ conformal field theory (CFT) action $S_{*}$ perturbed by a replica interaction of the form $$-\mathbb{S}=-\sum_{a=1}^{R}S_{*}^{(a)}+\Delta\int d^2 x \sum_{\substack{a,b=1\\ a\neq b}}^{R}\varphi^{(a)}(x)\varphi^{(b)}(x).$$ Here $\varphi$ is a scaling field belonging to the CFT with action $S_*$ and the coupling $\Delta$ is relevant in the RG sense. We show that the infrared value of $c_{\text{eff}}$ is always $\textit{less}$ than the central charge $c$ of the unperturbed CFT $S_{*}$. We refer to this result as the "$c$-effective theorem". As an application of this theorem, we consider replica field theories in the limit of $R \to 1$ replicas of the form above, shown by Nahum and Jacobsen [arXiv:2504.01264] to describe $2D$ classical monitored systems, where measurements introduce a form of quenched randomness via Bayes' theorem. Lastly, we discuss a possible relationship of our theorem with the effective central charge $c_{\text{eff}}^{(R\rightarrow0)}=(dc/dR)|_{R=0}$ for the above replica action in the different $R\rightarrow0$ replica limit, which is of relevance to systems with generic uncorrelated impurity-type quenched disorder, as opposed to measurements.

Related papers

• Universal and non-universal facets of quantum critical phenomena unveiled along the Schmidt decomposition theorem [0.0]
  We investigate the influence of the spin magnitude $S$ on the quantum Grneisen parameter $0textK_q$ right at critical points (CPs) for the 1D Ising model under a transverse magnetic field.<n>Our findings unveil both universal and non-universal aspects of quantum criticality in terms of $0textK_q$ and $S_q$.
  arXiv  Detail & Related papers  (2025-12-11T20:09:23Z)
• 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)
• Emergent random matrix universality in quantum operator dynamics [0.0]
  We prove the universality of eigenvalue correlations in random matrix theory.<n>We show that at low frequencies $G_n (z)$ is governed by the Bessel universality class from RMT.<n>We give a new numerical method, the spectral bootstrap, for approximating spectral functions from Lanczos coefficients.
  arXiv  Detail & Related papers  (2025-04-25T12:38:24Z)
• Monge-Kantorovich Fitting With Sobolev Budgets [6.748324975906262]
  We show that when $rho$ is concentrated near an $mtext-d$ set we may interpret this as a manifold learning problem with noisy data.<n>We quantify $nu$'s performance in approximating $rho$ via the Monge-Kantorovich $p$-cost $mathbbW_pp(rho, nu)$, and constrain the complexity by requiring $mathrmsupp nu$ to be coverable by an $f : mathbbRm
  arXiv  Detail & Related papers  (2024-09-25T01:30:16Z)
• Universal non-Hermitian flow in one-dimensional PT-symmetric quantum criticalities [5.402334522977581]
  We study the finite-size scaling of the energy of non-Hermitian Su-Schrieffer-Heeger model with parity and time-reversal symmetry. We find that under open boundary condition (OBC), the energy scaling $E(L)sim c/L$ reveals a negative central charge $c=-2$ at the non-Hermitian critical point. The scaling function demonstrates distinct behaviors at topologically non-trivial and trivial sides of critical points.
  arXiv  Detail & Related papers  (2024-05-02T18:02:13Z)
• On a Neural Implementation of Brenier's Polar Factorization [24.48716080522871]
  In 1991, Brenier proved a theorem that generalizes the polar decomposition for square matrices factored as PSD $times$ unitary -- to any vector field $F:mathbbRdright mathbbRdarrow.<n>We propose a practical implementation of the polar factorization theorem, and explore possible uses within machine learning.
  arXiv  Detail & Related papers  (2024-03-05T15:59:54Z)
• On the $O(\frac{\sqrt{d}}{T^{1/4}})$ Convergence Rate of RMSProp and Its Momentum Extension Measured by $\ell_1$ Norm [54.28350823319057]
  This paper considers the RMSProp and its momentum extension and establishes the convergence rate of $frac1Tsum_k=1T.<n>Our convergence rate matches the lower bound with respect to all the coefficients except the dimension $d$.<n>Our convergence rate can be considered to be analogous to the $frac1Tsum_k=1T.
  arXiv  Detail & Related papers  (2024-02-01T07:21:32Z)
• A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing [68.80803866919123]
  Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously. Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples. We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
  arXiv  Detail & Related papers  (2023-09-25T17:54:19Z)
• 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)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• Renormalization group for measurement and entanglement phase transitions [0.0]
  We analyze the renormalization-group (RG) flows of two effective Lagrangians. We show that the theory for the random tensor network formally possesses a dimensional reduction property analogous to that of the random-field Ising model.
  arXiv  Detail & Related papers  (2023-03-14T12:40:03Z)
• The Approximate Degree of DNF and CNF Formulas [95.94432031144716]
  For every $delta>0,$ we construct CNF and formulas of size with approximate degree $Omega(n1-delta),$ essentially matching the trivial upper bound of $n. We show that for every $delta>0$, these models require $Omega(n1-delta)$, $Omega(n/4kk2)1-delta$, and $Omega(n/4kk2)1-delta$, respectively.
  arXiv  Detail & Related papers  (2022-09-04T10:01:39Z)
• A New Look at the $C^{0}$-formulation of the Strong Cosmic Censorship Conjecture [68.8204255655161]
  We argue that for generic black hole parameters as initial conditions for Einstein equations, the metric is $C0$-extendable to a larger Lorentzian manifold. We prove it violates the "complexity=volume" conjecture for a low-temperature hyperbolic AdS$_d+1$ black hole dual to a CFT living on a ($d-1$)-dimensional hyperboloid $H_d-1$.
  arXiv  Detail & Related papers  (2022-06-17T12:14:33Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Reliability of lattice gauge theories in the thermodynamic limit [0.0]
  In quantum-simulation implementations of gauge theories it is compromised by experimental imperfections. We numerically demonstrate that robust gauge invariance is also retained through a single-body gauge-protection term.
  arXiv  Detail & Related papers  (2021-04-14T18:00:04Z)
• A General Derivative Identity for the Conditional Mean Estimator in Gaussian Noise and Some Applications [128.4391178665731]
  Several identities in the literature connect $E[bf X|bf Y=bf y]$ to other quantities such as the conditional variance, score functions, and higher-order conditional moments. The objective of this paper is to provide a unifying view of these identities.
  arXiv  Detail & Related papers  (2021-04-05T12:48:28Z)
• Universal tripartite entanglement in one-dimensional many-body systems [0.0]
  We introduce two related non-negative measures of tripartite entanglement $g$ and $h$. We prove structure theorems which show that states with nonzero $g$ or $h$ have nontrivial tripartite entanglement.
  arXiv  Detail & Related papers  (2020-11-24T02:59:14Z)
• Near-Optimal SQ Lower Bounds for Agnostically Learning Halfspaces and ReLUs under Gaussian Marginals [49.60752558064027]
  We study the fundamental problems of agnostically learning halfspaces and ReLUs under Gaussian marginals. Our lower bounds provide strong evidence that current upper bounds for these tasks are essentially best possible.
  arXiv  Detail & Related papers  (2020-06-29T17:10:10Z)
• Nearly Optimal Regret for Stochastic Linear Bandits with Heavy-Tailed Payoffs [35.988644745703645]
  We analyze the linear bandits with heavy-tailed payoffs, where the payoffs admit finite $1+epsilon$ moments. We propose two novel algorithms which enjoy a sublinear regret bound of $widetildeO(dfrac12Tfrac11+epsilon)$.
  arXiv  Detail & Related papers  (2020-04-28T13:01:38Z)
• Robust Interference Management for SISO Systems with Multiple Over-the-Air Computations [16.52374405363812]
  We consider the over-the-air computation of sums over a shared complex-valued MAC. Finding appropriate Tx-Rx scaling factors balance between a low error in the computation of $s_n$ and the interference induced by it.
  arXiv  Detail & Related papers  (2020-04-21T11:15:26Z)
• A closer look at the approximation capabilities of neural networks [6.09170287691728]
  A feedforward neural network with one hidden layer is able to approximate any continuous function $f$ to any given approximation threshold $varepsilon$. We show that this uniform approximation property still holds even under seemingly strong conditions imposed on the weights.
  arXiv  Detail & Related papers  (2020-02-16T04:58:43Z)
• Curse of Dimensionality on Randomized Smoothing for Certifiable Robustness [151.67113334248464]
  We show that extending the smoothing technique to defend against other attack models can be challenging. We present experimental results on CIFAR to validate our theory.
  arXiv  Detail & Related papers  (2020-02-08T22:02:14Z)

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.