Detecting emergent continuous symmetries at quantum criticality

Abstract

New or enlarged symmetries can emerge at the low-energy spectrum of a Hamiltonian that does not possess the symmetries, if the symmetry breaking terms in the Hamiltonian are irrelevant under the renormalization group flow. In this letter, we propose a tensor network based algorithm to numerically extract lattice operator approximation of the emergent conserved currents from the ground state of any quantum spin chains, without the necessity to have prior knowledge about its low-energy effective field theory. Our results for the spin-1/2 $J$-$Q$ Heisenberg chain and a one-dimensional version of the deconfined quantum critical points (DQCP) demonstrate the power of our method to obtain the emergent lattice Kac-Moody generators. It can also be viewed as a way to find the local integrals of motion of an integrable model and the local parent Hamiltonian of a critical gapless ground state.

arXiv comment7+13 pages; results and figures have been updated with Hermiticity imposed

References in corpus (34)

• "Deconfined" quantum critical points
• Local conservation laws and the structure of the many-body localized states
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Tensor networks for complex quantum systems
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Scaling of entanglement support for Matrix Product States
• Algebraic spin liquid as the mother of many competing orders
• Variational optimization algorithms for uniform matrix product states
• Does a single eigenstate encode the full Hamiltonian?
• Tangent-space methods for uniform matrix product states
• Critical level crossings and gapless spin liquid in the square-lattice spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet
• Applying matrix product operators to model systems with long-range interactions
• Variational matrix product ansatz for dispersion relations
• Finite automata for caching in matrix product algorithms
• Determining a local Hamiltonian from a single eigenstate
• Excitations and the tangent space of projected entangled-pair states
• Computational inverse method for constructing spaces of quantum models from wave functions
• Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain: Analogies to deconfined quantum critical points
• Deconfined quantum critical point in one dimension
• Simulating excitation spectra with projected entangled-pair states
• Precise extrapolation of the correlation function asymptotics in uniform tensor network states with application to the Bose-Hubbard and XXZ models
• Emergent Symmetry and Conserved Current at a One Dimensional Incarnation of Deconfined Quantum Critical Point
• Emmy Noether looks at the deconfined quantum critical point
• Local Matrix Product Operators: Canonical Form, Compression, & Control Theory
• Method to characterize spinons as emergent elementary particles
• Integrals of motion of the Haldane Shastry Model
• Universal entropy of conformal critical theories on a Klein bottle
• Local conservation laws in spin-1/2 XY chains with open boundary conditions
• Vacancy-induced spin texture in a one dimensional $S=1/2$ Heisenberg antiferromagnet
• Numerical Methods for Detecting Symmetries and Commutant Algebras
• Numerical Investigations of SO(4) Emergent Extended Symmetry in Spin-1/2 Heisenberg Antiferromagnetic Chains
• Emergence of Kac-Moody Symmetry in Critical Quantum Spin Chains

Cited by in corpus (6)

• Tangent space generators of matrix product states and exact Floquet quantum scars
• Probing universal critical scaling with scan-DMRG
• Kac-Moody symmetries in one-dimensional bosonic systems
• Robustness of critical U(1) spin liquids and emergent symmetries in tensor networks
• Ground-State-Based Model Reduction with Unitary Circuits
• Entanglement scaling and criticality of infinite-size quantum many-body systems in continuous space addressed by a tensor network approach