Abstract
Continuous quantum phase transitions beyond the conventional paradigm of fluctuations of a symmetry-breaking order parameter are challenging for theory. These phase transitions often involve emergent deconfined gauge fields at the critical points as demonstrated in phase transitions between different broken-symmetry states of 2+1-dimensional quantum magnets, as well as those between symmetry-protected topological (SPT) phases. In this paper, we present several examples of deconfined quantum critical points between SPT phases in 3+1-D for both bosonic and fermionic systems. These critical theories can be formulated as non-Abelian gauge theories either in the infrared-free regime or in the conformal window when they flow to the Banks-Zaks fixed points. We explicitly demonstrate several interesting quantum critical phenomena. We describe situations in which the same phase transition allows for multiple universality classes controlled by distinct fixed points. We exhibit the possibility—which we dub “unnecessary quantum critical points”—of stable generic continuous phase transitions within the same phase. We present examples of interaction-driven, band-theory-forbidden, continuous phase transitions between two distinct band insulators. The understanding we develop leads us to suggest an interesting possible 3+1-D field theory duality between SU(2) gauge theory coupled to one massless adjoint Dirac fermion and the theory of a single massless Dirac fermion augmented by a decoupled topological field theory.3 MoreReceived 2 January 2019Revised 2 April 2019DOI:https://doi.org/10.1103/PhysRevX.9.021034Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCritical phenomenaDualities in field theoryNon-Abelian gauge theoriesSymmetry protected topological statesTopological insulatorsTopological phase transitionCondensed Matter, Materials & Applied PhysicsParticles & Fields
Highlights
Ground states of quantum many-particle systems can go through phase transitions as the Hamiltonian is tuned. When such a quantum phase transition is continuous, the resulting quantum critical point has many interesting properties, which have been explored for many decades [1,2] in diverse contexts
We show how to interpret them as quantum critical points in the phase diagram of the “microscopic” d.o.f. of the system, similar to what we reviewed for the free massless Dirac fermion theories in the previous section
In all cases we study, these massless gauge theories provide valuable examples of quantum critical points associated with phase transitions between trivial and symmetry-protected topological (SPT) phases of the underlying boson or fermion system
Summary
Ground states of quantum many-particle systems can go through phase transitions as the Hamiltonian is tuned When such a quantum phase transition is continuous, the resulting quantum critical point has many interesting properties, which have been explored for many decades [1,2] in diverse contexts. We describe examples of interaction-driven topological phase transitions that are not possible within a free fermion description, even though the phases themselves can be described by free fermions These transitions violate band theory rules for which band insulators can be separated by continuous phase transitions. We show that an SUð2Þ gauge theory coupled to one massless adjoint Dirac fermion and massive fundamental bosons may share the same infrared (IR) physics with a theory of a free Dirac fermion supplemented by a gapped topological field theory Both theories have the same local operators and the same global symmetries and anomalies. There are no simple dualities of nonsupersymmetric theories that are known to us in 3 þ 1-D
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