May 15, 2024
We utilize the topological holographic framework to characterize and gain insights into the nature of quantum critical points and gapless phases in fermionic quantum systems. Topological holography is a general framework that describes the generalized global symmetry and the symmetry charges of a local quantum system in terms of a slab of a topological order, termed as the symmetry topological field theory (SymTFT), in one higher dimension. In this work, we consider a generalization of the topological holographic picture for $(1+1)d$ fermionic quantum phases of matter. We discuss how spin structures are encoded in the SymTFT and establish the connection between the formal fermionization formula in quantum field theory and the choice of fermionic gapped boundary conditions of the SymTFT. We demonstrate the identification and the characterization of the fermionic gapped phases and phase transitions through detailed analysis of various examples, including the fermionic systems with $\mathbb{Z}_{2}^{F}$, $\mathbb{Z}_{2} \times \mathbb{Z}_{2}^{F}$, $\mathbb{Z}_{4}^{F}$, and the fermionic version of the non-invertible $\text{Rep}(S_{3})$ symmetry. Our work uncovers many exotic fermionic quantum critical points and gapless phases, including two kinds of fermionic symmetry enriched quantum critical points, a fermionic gapless symmetry protected topological (SPT) phase, and a fermionic gapless spontaneous symmetry breaking (SSB) phase that breaks the fermionic non-invertible symmetry.
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Topological holography is a conjectured correspondence between the symmetry charges and defects of a $D$-dimensional system with the anyons in a $(D+1)$-dimensional topological order: the symmetry topological field theory (SymTFT). Topological holography is conjectured to capture the topological aspects of symmetry in gapped and gapless systems, with different phases corresponding to different gapped boundaries (anyon condensations) of the SymTFT. This correspondence was prev...
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In an earlier work we developed a holographic theory for the phase transition between bosonic symmetry-protected topological (SPT) states. This paper is a continuation of it. Here we present the holographic theory for fermionic SPT phase transitions. We show that in any dimension $ d $, the critical states of fermionic SPT phase transitions has an emergent $Z_2^T$ symmetry and can be realized on the boundary of a $ d+1 $-dimensional bulk SPT with an extra $Z_2^T$ symmetry.
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Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local dynamics of a theory and provides a unified description of the symmetry and duality in gapped and gapless phases of matter. In this work, we develop the topological holographic picture for (1+1)d quantum phases, including both gapped phase...
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Symmetry topological field theory (SymTFT) gives a holographic correspondence between systems with a global symmetry and a higher-dimensional topological field theory. In this framework, classification of gapped phases of matter in spacetime dimension 1+1D correspond to classifications of mechanisms to confine the SymTFT by condensing anyons. In this work, we extend these results to characterize gapless symmetry-protected topological states: symmetry-enriched gapless phases o...
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Continuous quantum phase transitions that are 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 2+1-dimensions. Examples include phase transitions in quantum magnetism as well as those between Symmetry Protected Topological phases. In this paper, we present several examples of Deconfined Quantum Crit...
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