Real-time Scattering in φ^4 Theory using Matrix Product States

• URL: http://arxiv.org/abs/2511.15697v1
• Date: Wed, 19 Nov 2025 18:55:00 GMT
• Title: Real-time Scattering in φ^4 Theory using Matrix Product States
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the critical behavior and real-time scattering dynamics of the interacting $φ^4$ quantum field theory in $(1+1)$ dimensions using uniform matrix product states and the time-dependent variational principle. A finite-entanglement scaling analysis at $λ= 0.8$ bounds the critical mass-squared to $μ_c^2 \in [-0.3190,-0.3185]$ and provides a quantitative map of the symmetric, near-critical, weakly broken, and deeply broken regimes. Using these ground states as asymptotic vacua, we simulate two-particle collisions in a sandwich geometry and extract the elastic scattering probability $P_{11\to 11}(E)$ and Wigner time delay $Δt(E)$ following the prescription of Jha et al. [Phys. Rev. Research 7, 023266 (2025)]. We find strongly inelastic scattering in the symmetric phase ($P_{11\to 11} \simeq 0.63$, $Δt \simeq -180$ for $μ^2 = 0.2$), almost perfectly elastic collisions in the spontaneously broken phase ($P_{11\to 11} \simeq 0.998$, $Δt \simeq -270$ for $μ^2=-0.2$ and $P_{11\to 11} \simeq 1$, $Δt \simeq -177.781$ for $μ^2=-0.5$), and a breakdown of the sandwich evolution precisely at the critical coupling, which provides a dynamical signature of the quantum critical point. These results demonstrate that TDVP-based uniform matrix product states can probe nonperturbative scattering and critical dynamics in lattice $φ^4$ theory with controlled entanglement truncation.

Related papers

• Correlation versus Causation in Quantum Criticality [0.0]
  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 $1/L25$.
  arXiv  Detail & Related papers  (2026-08-13T03:27:28Z)
• The Collapse of Unentangled Stoquastic Merlin-Arthur Proof Systems [46.657699628769336]
  Entanglement and interference are among the most fundamental properties of quantum mechanics.<n>We prove that entanglement gives no additional power to stoquastic verification.
  arXiv  Detail & Related papers  (2026-05-15T17:52:33Z)
• OAM-Induced Lattice Rotation Reveals a Fractional Optimum in Fault-Tolerant GKP Quantum Sensing [0.0]
  We establish that orbital-angular-momentum encoding and Gottesman-Kitaev-Preskill (GKP) lattice geometry are structurally coupled.<n>Using an end-to-end differentiable Strawberry Fields--TensorFlow circuit, we jointly optimise $ell$, the lattice aspect ratio $r$, and the finite-energy envelope $$ to maximise quantum Fisher information.
  arXiv  Detail & Related papers  (2026-05-13T09:49:16Z)
• Weight-Decay Turns Transformer Loss Landscapes Villani: Functional-Analytic Foundations for Optimization and Generalization [2.9582724435853858]
  This paper provides the first rigorous functional-analytic characterization of the standard Transformer objective--cross-entropy loss with $L2$ regularization.<n>We show that the regularized loss $mathcalF$ is infinitely differentiable, grows at least quadratically, has Gaussian-integrable tails, and satisfies the differential growth condition $-mathcalF + tfrac1s|nablamathcalF|2 to infty$ as $|| to
  arXiv  Detail & Related papers  (2026-05-07T17:22:19Z)
• 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)
• Exact Solvability and Integrability Signatures in a Periodically Driven Infinite-Range Spin Chain: The Case of Floquet interval $π/2$ [0.5716454975957338]
  We study the signatures of quantum integrability (QI) in a spin chain model.<n>We analyze the unitary operator, its eigensystem, the single-qubit reduced density matrix, and the entanglement dynamics for arbitrary initial state for any $N$.
  arXiv  Detail & Related papers  (2025-09-24T10:50:56Z)
• Controlling Symmetries and Quantum Criticality in the Anisotropic Coupled-Top Model [32.553027955412986]
  We investigate the anisotropic coupled-top model, which describes the interactions between two large spins along both $x-$ and $y-$directions.<n>We can manipulate the system's symmetry, inducing either discrete $Z$ or continuous U(1) symmetry.<n>The framework provides an ideal platform for experimentally controlling symmetries and investigating associated physical phenomena.
  arXiv  Detail & Related papers  (2025-02-13T15:14:29Z)
• Analytical Correlation in the H$_{2}$ Molecule from the Independent Atom Ansatz [49.1574468325115]
  The total energy functional correctly dissociates the H-H bond and yields absolute errors of 0.002 $rA$, 0.19 eV, and 13 cm-1$ relative to experiment at the tight binding computational cost. The chemical bond formation is attributed to the Heitler-London resonance of quasi-orthogonal atomic states with no contributions from kinetic energy or charge accumulation in the bond.
  arXiv  Detail & Related papers  (2024-05-20T21:21:42Z)
• Walking behavior induced by $\mathcal{PT}$ symmetry breaking in a non-Hermitian $\ m XY$ model with clock anisotropy [0.0]
  A quantum system governed by a non-Hermitian Hamiltonian may exhibit zero temperature phase transitions driven by interactions.<n>We show that when the $mathcalPT$ symmetry is broken, and time-evolution becomes non-unitary, a scaling behavior similar to the Berezinskii-Kosterlitz-Thouless phase transition ensues.
  arXiv  Detail & Related papers  (2024-04-26T12:45:16Z)
• Towards the "puzzle" of Chromium dimer Cr$_2$: predicting the Born-Oppenheimer rovibrational spectrum [44.99833362998488]
  This paper calculates the potential energy curve for the state $X1Sigma+$ of the Cr$$$ dimer. It is found for the first time for the whole range of internuclear distances $R$.
  arXiv  Detail & Related papers  (2024-01-06T17:00:12Z)
• 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)
• On parametric resonance in the laser action [91.3755431537592]
  We consider the selfconsistent semiclassical Maxwell--Schr"odinger system for the solid state laser. We introduce the corresponding Poincar'e map $P$ and consider the differential $DP(Y0)$ at suitable stationary state $Y0$.
  arXiv  Detail & Related papers  (2022-08-22T09:43:57Z)
• Near-optimal fitting of ellipsoids to random points [68.12685213894112]
  A basic problem of fitting an ellipsoid to random points has connections to low-rank matrix decompositions, independent component analysis, and principal component analysis. We resolve this conjecture up to logarithmic factors by constructing a fitting ellipsoid for some $n = Omega(, d2/mathrmpolylog(d),)$. Our proof demonstrates feasibility of the least squares construction of Saunderson et al. using a convenient decomposition of a certain non-standard random matrix.
  arXiv  Detail & Related papers  (2022-08-19T18:00:34Z)
• Symmetry-resolved entanglement entropy in critical free-fermion chains [0.0]
  symmetry-resolved R'enyi entanglement entropy is known to have rich theoretical connections to conformal field theory. We consider a class of critical quantum chains with a microscopic U(1) symmetry. For the density matrix, $rho_A$, of subsystems of $L$ neighbouring sites we calculate the leading terms in the large $L$ expansion of the symmetry-resolved R'enyi entanglement entropies.
  arXiv  Detail & Related papers  (2022-02-23T19:00:03Z)
• Exact one- and two-site reduced dynamics in a finite-size quantum Ising ring after a quench: A semi-analytical approach [4.911435444514558]
  We study the non-equilibrium dynamics of a homogeneous quantum Ising ring after a quench. The long-timescale reduced dynamics of a single spin and of two nearest-neighbor spins is studied.
  arXiv  Detail & Related papers  (2021-03-23T13:14:50Z)
• Anharmonic oscillator: a solution [77.34726150561087]
  The dynamics in $x$-space and in $(gx)-space corresponds to the same energy spectrum with effective coupling constant $hbar g2$. A 2-classical generalization leads to a uniform approximation of the wavefunction in $x$-space with unprecedented accuracy.
  arXiv  Detail & Related papers  (2020-11-29T22:13:08Z)

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.