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Exactly Solvable Model for a Deconfined Quantum Critical Point in 1D
Carolyn Zhang1, Michael Levin1
1Department of Physics, Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA.
Physical Review Letters
|January 27, 2023
Summary
We developed an exactly solvable model for a deconfined quantum critical point (DQCP) in 1+1 dimensions. This model reveals DQCPs are linked to Z4 symmetry breaking critical points at the edge of a 2+1 dimensional topological phase.
Area of Science:
- Condensed Matter Physics
- Quantum Field Theory
- Topological Phases of Matter
Background:
- Deconfined quantum critical points (DQCPs) represent exotic transitions between distinct quantum phases.
- Symmetry Protected Topological (SPT) phases offer unique boundary phenomena.
- Understanding DQCPs in lower dimensions is crucial for theoretical advancements.
Purpose of the Study:
- To construct an exactly solvable lattice model for a DQCP in (1+1) dimensions.
- To investigate the unusual setting of a DQCP at the edge of a (2+1) dimensional bosonic SPT phase.
- To establish a connection between DQCPs and Z4 symmetry breaking critical points.
Main Methods:
- Construction of an exactly solvable lattice model.
- Utilizing an exact mapping between the SPT edge theory and a Z4 spin chain.
- Analysis of phase transitions in (1+1) and (2+1) dimensional systems.
Main Results:
- An exactly solvable lattice model for a DQCP in (1+1) dimensions is successfully constructed.
- The DQCP is found to occur at the edge of a (2+1) dimensional bosonic SPT phase with Z2×Z2 symmetry.
- The study reveals a direct relationship between these DQCPs and ordinary Z4 symmetry breaking critical points.
Conclusions:
- The developed model provides a tractable framework for studying DQCPs in novel contexts.
- The findings highlight the intricate relationship between topological phases and quantum criticality.
- This work bridges the understanding of DQCPs and conventional symmetry breaking phenomena.
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