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Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids · Around

2016

Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids

Pretko, Michael

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Spin liquids are conventionally described by gauge theories with a vector gauge field.

However, there exists a wider class of spin liquids with higher rank tensors as the gauge variable.
In this work, we focus on (3+1)-dimensional spin liquids described by U(1) symmetric tensor gauge theories, which have recently been shown to be stable gapless spin liquids.
We investigate the particle structure of these tensor gauge theories and find that they have deep connections with the "fracton" models recently discovered by Vijay, Haah, and Fu.

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We here use “spin” in a generalized sense referring to any bosonic degrees of freedom, including conventional spins (with a specific behavior under rotations), rotors, itinerant bosons, or simply a general discrete-leveled object (qudit). The highly entangled phases of any of these can be described in a unified framework via deconfined gauge theories. Even the case of fermionic microscopic degrees of freedom is only mildly different. “Long-range entangled phase” may be more accurate, but we stick with “spin liquid” for now, to keep closer contact with existing literature

Cited in the paper.

The lower critical spatial dimension for deconfinement of a rank n n compact U ⁡ ( 1 ) U(1) antisymmetric tensor gauge theory is 2 + n 2+n . In a higher-dimensional world, we would have lots of string-theoretic spin liquids to study

Cited in the paper.

It should be noted that U ⁡ ( 1 ) U(1) does not seem to represent a “gauge group” of the theory, as these theories are outside the conventional Yang-Mills Lie algebra framework. As we will see, there are no conventional matter fields transforming under a group representation. We use the terminology U ⁡ ( 1 ) U(1) only to indicate the values of the gauge variable, which may not be ideal. One would expect that a better naming convention will arise from a more formal mathematical classification of these sorts of gauge theories, analogous to the Lie algebra framework for the rank 1 case. We hope that the sins of the present naming convention are not overly severe

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