Order, Disorder, and Transitions in Decorated AKLT States on Bethe Lattices

• URL: http://arxiv.org/abs/2103.11819v1
• Date: Mon, 22 Mar 2021 17:35:18 GMT
• Title: Order, Disorder, and Transitions in Decorated AKLT States on Bethe Lattices
• Abstract summary: We extend prior analysis on the Bethe lattice (or Cayley tree) to a variant with a series of $n$ spin-1 decorations placed on each edge. The recurrence relations derived for this system demonstrate that such systems are critical for coordination numbers $z=3n+1$, demonstrating order for greater and disorder for lesser coordination number.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Returning to one of the original generalizations of the AKLT state, we extend prior analysis on the Bethe lattice (or Cayley tree) to a variant with a series of $n$ spin-1 decorations placed on each edge. The recurrence relations derived for this system demonstrate that such systems are critical for coordination numbers $z=3^{n+1}$, demonstrating order for greater and disorder for lesser coordination number. We then generalize further, effectively interpolating between systems with different values of $n$, using two realizations, one isotropic under local $SU(2)$ transformations and one anisotropic. Exact analysis of these recurrence relations allows us to deduce the location and behavior of order-disorder phase transitions for $z>4$.

Related papers

• $\ ext{GSF-}χ$: Global Stereochemical Fields for Chiral Graph Transformers [49.85093436361195]
  We introduce GSF-$$, a graph transformer in which stereogenic units modulate all pairwise interactions.<n>A $C$ projection separates mirror-even ECD peak counts and positions from mirror-odd peak signs.<n>GSF-$$ leads every central-ECD output and improves axial Rotation and Symbol by $12.6%$ and $7.9%$ over the strongest baseline.
  arXiv  Detail & Related papers  (2026-09-11T07:41:20Z)
• Nonlocality-induced critical-length hierarchy from non-Hermitian competition [48.9823527611878]
  In short-range systems formed by two coupled chains, competition leads to the critical-length law $N_csimln D$.<n>Here we show that long-range hoppings fundamentally reorganizes this critical behavior, producing a hierarchy of distinct scaling laws.<n>Our results offer a platform-independent framework testable in programmable topoelectrical circuits, photonic lattices and digital quantum simulators.
  arXiv  Detail & Related papers  (2026-08-03T18:00:18Z)
• Stabilizing Fixed-Point Iteration for Markov Chain Poisson Equations [49.702772230127465]
  We study finite-state Markov chains with $n$ states and transition matrix $P$.<n>We show that all non-decaying modes are captured by a real peripheral invariant subspace $mathcalK(P)$, and that the induced operator on the quotient space $mathbbRn/mathcalK(P) is strictly contractive, yielding a unique quotient solution.
  arXiv  Detail & Related papers  (2026-01-31T02:57:01Z)
• Accurate ground states of $SU(2)$ lattice gauge theory in 2+1D and 3+1D [0.7999703756441757]
  We present a neural network wavefunction framework for solving non-Abelian lattice gauge theories in a continuous group representation.<n>We learn a parameterization of the ground state wavefunction of $SU(2)$ lattice gauge theory in 2+1 and 3+1 dimensions.<n>Our method opens up an avenue for studying lattice gauge theories beyond one dimension, with efficient scaling to larger systems.
  arXiv  Detail & Related papers  (2025-09-15T18:00:17Z)
• Correlators in phase-ordering from Schrödinger-invariance [0.0]
  Systems undergoing phase-ordering kinetics undergo phase-ordering kinetics after a quench into the ordered phase with $0TT_c$ from a fully disordered initial state.<n>The long-time behaviour of their single-time and two-time correlators, determined by the noisy initial conditions, is derived from Schr"odinger-invariance.<n>The scaling in fully finite systems and of global correlators is found and the low-temperature generalisation $lambda= d-2Theta$ of the Janssen-Schaub-Schmittmann scaling relation is derived
  arXiv  Detail & Related papers  (2025-08-12T14:30:26Z)
• 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)
• Extracting topological spins from bulk multipartite entanglement [0.0]
  We describe a series of bulk multipartite entanglement measures that extract the invariants $sum_a d_a2 theta_ar$ for any $r geq 2$.<n>These invariants are obtained as expectation values of permutation operators between $2r$ replicas of the wavefunction.<n>Our proposed measures provide a refined tool for distinguishing topological phases, capturing information beyond conventional entanglement measures.
  arXiv  Detail & Related papers  (2025-02-17T19:02:19Z)
• Ehrenfeucht-Haussler Rank and Chain of Thought [51.33559894954108]
  We show that the rank of a function $f$ corresponds to the minimum number of Chain of Thought steps required by a single-layer transformer decoder. We also analyze the problem of identifying the position of the $k$-th occurrence of 1 in a Boolean sequence, proving that it requires $k$ CoT steps.
  arXiv  Detail & Related papers  (2025-01-22T16:30:58Z)
• Decoherence and wavefunction deformation of $D_4$ non-Abelian topological order [0.0]
  We show that certain non-Abelian TOs can be analyzed and understood to a similar degree, despite being significantly richer. By identifying the corresponding local statistical mechanical spin or rotor model with $D_4$ symmetry, we find a remarkable stability against proliferating non-Abelian anyons.
  arXiv  Detail & Related papers  (2024-09-19T17:56:21Z)
• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Optimization of Time-Dependent Decoherence Rates and Coherent Control for a Qutrit System [77.34726150561087]
  Incoherent control makes the decoherence rates depending on time in a specific controlled manner. We consider the problem of maximizing the Hilbert-Schmidt overlap between the system's final state $rho(T)$ and a given target state $rho_rm target.
  arXiv  Detail & Related papers  (2023-08-08T01:28:50Z)
• Quantum dichotomies and coherent thermodynamics beyond first-order asymptotics [9.437165725355701]
  We address the problem of exact and approximate transformation of quantum dichotomies in the thermodynamic regime. We derive second-order expressions for the optimal transformation rate $R_n$ in the small, moderate, and large deviation error regimes. What is more, our result on quantum dichotomies can also be used to obtain, up to second-order terms, optimal conversion rates between pure bipartite entangled states under local operations and classical communication.
  arXiv  Detail & Related papers  (2023-03-09T19:00:01Z)
• Localization measures of parity adapted U($D$)-spin coherent states applied to the phase space analysis of the $D$-level Lipkin-Meshkov-Glick model [0.0]
  We study phase-space properties of critical, parity symmetric, $N$-quDit systems undergoing a quantum phase transition. For finite $N$, parity can be restored by projecting DSCS onto $2D-1$ different parity invariant subspaces. Pres of the QPT are then visualized for finite $N$ by plotting the Husimi function of these parity projected DSCS in phase space.
  arXiv  Detail & Related papers  (2023-02-13T10:51:19Z)
• Self-healing of Trotter error in digital adiabatic state preparation [52.77024349608834]
  We prove that the first-order Trotterization of a complete adiabatic evolution has a cumulative infidelity that scales as $mathcal O(T-2 delta t2)$ instead of $mathcal O(T2delta t2)$ expected from general Trotter error bounds. This result suggests a self-healing mechanism and explains why, despite increasing $T$, infidelities for fixed-$delta t$ digitized evolutions still decrease for a wide variety of Hamiltonians.
  arXiv  Detail & Related papers  (2022-09-13T18:05:07Z)
• Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping [45.873301228345696]
  localization problem in the crossover regime for the dimension $d=2$ and hopping $V(r) propto r-2$ is not resolved yet. We show that for the hopping determined by two-dimensional anisotropic dipole-dipole interactions there exist two distinguishable phases at weak and strong disorder.
  arXiv  Detail & Related papers  (2022-05-29T16:53:20Z)
• Neural Inverse Kinematics [72.85330210991508]
  Inverse kinematic (IK) methods recover the parameters of the joints, given the desired position of selected elements in the kinematic chain. We propose a neural IK method that employs the hierarchical structure of the problem to sequentially sample valid joint angles conditioned on the desired position.
  arXiv  Detail & Related papers  (2022-05-22T14:44:07Z)
• Light transfer transitions beyond higher-order exceptional points in parity-time and anti-parity-time symmetric waveguide arrays [7.21172766653517]
  Two non-Hermitian arrays are proposed for investigating light transfer dynamics based on $N$th-order exceptional points (EPs) The $mathcalPT$-symmetric array supports two $N$th-order EPs separating an unbroken and a broken phase with real and imaginary eignvalues, respectively. The anti-$mathcalPT$-symmetric array supports also two $N$th-order EPs separating an unbroken and a broken phase, which refer however to imaginary and real eignvalues, respectively.
  arXiv  Detail & Related papers  (2022-05-16T10:51:38Z)
• 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)
• Dynamical Signatures of Chaos to Integrability Crossover in $2\times 2$ Generalized Random Matrix Ensembles [0.0]
  We study the energy correlations by calculating the density and 2nd moment of the Nearest Neighbor Spacing (NNS) We observe that for large $N$ the 2nd moment of NNS and the relative depth of the correlation hole exhibit a second order phase transition at $gamma=2$.
  arXiv  Detail & Related papers  (2020-10-28T05:02:13Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

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.