Related papers: Entanglement scaling for $\lambda\phi

Entanglement scaling for $\lambda\phi_2^4$

URL: http://arxiv.org/abs/2104.10564v3
Date: Thu, 17 Nov 2022 13:01:33 GMT
Title: Entanglement scaling for $\lambda\phi_2^4$
Authors: Bram Vanhecke, Frank Verstraete, Karel Van Acoleyen
Abstract summary: We show that the order parameter $phi$, the correlation length $xi$ and quantities like $phi3$ and the entanglement entropy exhibit useful double scaling properties. We find the value $alpha_c=11.09698(31)$ for the critical point, improving on previous results.
Score: 0.0
License: http://creativecommons.org/publicdomain/zero/1.0/
Abstract: We study the $\lambda\phi^4$ model in $0+2$ dimensions at criticality, and effectuate a simultaneous scaling of UV and IR physics. We demonstrate that the order parameter $\phi$, the correlation length $\xi$ and quantities like $\phi^3$ and the entanglement entropy exhibit useful double scaling properties. The calculations are performed with boundary matrix product state methods on tensor network representations of the partition function, though the technique is equally applicable outside the realm of tensor networks. We find the value $\alpha_c=11.09698(31)$ for the critical point, improving on previous results.

Related papers

Bayesian Inference with Deep Weakly Nonlinear Networks [57.95116787699412]
We show at a physics level of rigor that Bayesian inference with a fully connected neural network is solvable. We provide techniques to compute the model evidence and posterior to arbitrary order in $1/N$ and at arbitrary temperature.
arXiv Detail & Related papers (2024-05-26T17:08:04Z)
On the $O(\frac{\sqrt{d}}{T^{1/4}})$ Convergence Rate of RMSProp and Its Momentum Extension Measured by $\ell_1$ Norm [59.65871549878937]
This paper considers the RMSProp and its momentum extension and establishes the convergence rate of $frac1Tsum_k=1T. Our convergence rate matches the lower bound with respect to all the coefficients except the dimension $d$. Our convergence rate can be considered to be analogous to the $frac1Tsum_k=1T.
arXiv Detail & Related papers (2024-02-01T07:21:32Z)
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)
Depth Dependence of $\mu$P Learning Rates in ReLU MLPs [72.14317069090407]
We study the dependence on $n$ and $L$ of the maximal update ($mu$P) learning rate. We find that it has a non-trivial dependence of $L$, scaling like $L-3/2.$
arXiv Detail & Related papers (2023-05-13T01:10:49Z)
High-dimensional Asymptotics of Feature Learning: How One Gradient Step Improves the Representation [89.21686761957383]
We study the first gradient descent step on the first-layer parameters $boldsymbolW$ in a two-layer network. Our results demonstrate that even one step can lead to a considerable advantage over random features.
arXiv Detail & Related papers (2022-05-03T12:09:59Z)
Quantum-information theory of a Dirichlet ring with Aharonov-Bohm field [0.0]
Shannon information entropies $S_rho,gamma$, Fisher informations $I_rho,gamma$, Onicescu energies $O_rho,gamma$ and R'enyi entropies $R_rho,gamma(alpha)$ are calculated.
arXiv Detail & Related papers (2022-02-09T19:26:56Z)
Crosstalk- and charge-noise-induced multiqubit decoherence in exchange-coupled quantum dot spin qubit arrays [0.0]
We determine the interqubit crosstalk- and charge-noise-induced decoherence time $Tast$ for a system of $L$ exchange-coupled electronic spin qubits. We calculate the expectation value of one of the spins, the Hamming distance, and the entanglement entropy and show that they are good proxies for the return probability for measuring $Tast$.
arXiv Detail & Related papers (2021-12-15T18:59:59Z)
How isotropic kernels perform on simple invariants [0.5729426778193397]
We investigate how the training curve of isotropic kernel methods depends on the symmetry of the task to be learned. We show that for large bandwidth, $beta = fracd-1+xi3d-3+xi$, where $xiin (0,2)$ is the exponent characterizing the stripe of the kernel at the origin.
arXiv Detail & Related papers (2020-06-17T09:59:18Z)
Linear Time Sinkhorn Divergences using Positive Features [51.50788603386766]
Solving optimal transport with an entropic regularization requires computing a $ntimes n$ kernel matrix that is repeatedly applied to a vector. We propose to use instead ground costs of the form $c(x,y)=-logdotpvarphi(x)varphi(y)$ where $varphi$ is a map from the ground space onto the positive orthant $RRr_+$, with $rll n$.
arXiv Detail & Related papers (2020-06-12T10:21:40Z)

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