Bulk Entanglement Spectrum: From Topological States to Quantum Criticality Speaker(s): Timothy Hsieh
Abstract: A quantum phase transition is usually achieved by tuning physical parameters in a Hamiltonian at zero temperature. Here, we demonstrate that the ground state of a topological phase itself encodes critical properties of its transition to a trivial phase. To extract this information, we introduce a partition of the system into two subsystems both of which extend throughout the bulk in all directions. The resulting bulk entanglement spectrum (BES) has a lowlying part that resembles the excitation spectrum of a bulk Hamiltonian, which allows us to probe a topological phase transition from a single wavefunction by tuning either the geometry of the partition or the entanglement temperature. As an example, this remarkable correspondence between topological phase transition and entanglement criticality is rigorously established for integer quantum Hall states. We also implement BES using tensor networks, derive the universality classes of topological phase transitions from the spin1 chain Haldane phase, and demonstrate that the AKLT wavefunction (and its generalizations) remarkably contains critical sixvertex (and in general eightvertex) models within it.
Date: 14/10/2014  3:30 pm
Series: Condensed Matter
