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.

7+13 pages; results and figures have been updated with Hermiticity imposed

References in corpus (10)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Scaling of entanglement support for Matrix Product States
• Algebraic spin liquid as the mother of many competing orders
• Applying matrix product operators to model systems with long-range interactions
• Finite automata for caching in matrix product algorithms
• Deconfined quantum critical point in one dimension
• Universal entropy of conformal critical theories on a Klein bottle
• Numerical Methods for Detecting Symmetries and Commutant Algebras

Cited by in corpus (5)

• 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
• 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