Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: The Parent State of Quantum Phases

Abstract

The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics. However, except for certain limits (for instance, a large number of flavors of matter fields), analytical methods can provide few concrete results. Here we show that the problem of compactU(1)lattice gauge theory coupled to fermionic matter in(2+1)Dis possible to access via sign-problem-free quantum Monte Carlo simulations. One can hence map out the phase diagram as a function of fermion flavors and the strength of gauge fluctuations. By increasing the coupling constant of the gauge field, gauge confinement in the form of various spontaneous-symmetry-breaking phases such as the valence-bond solid (VBS) and Néel antiferromagnet emerge. Deconfined phases with algebraic spin and VBS correlation functions are also observed. Such deconfined phases are incarnations of exotic states of matter, i.e., the algebraic spin liquid, which is generally viewed as the parent state of various quantum phases. The phase transitions between the deconfined and confined phases, as well as that between the different confined phases provide various manifestations of deconfined quantum criticality. In particular, for four flavorsNf=4, our data suggest a continuous quantum phase transition between the VBS and Néel order. We also provide preliminary theoretical analysis for these quantum phase transitions.

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Plain Language Summary

An exotic 2D state of matter known as a U(1) Dirac spin liquid could help condensed-matter physicists explain perplexing observations of many high-temperature superconductors and frustrated magnets. High-energy physicists are also interested in these spin liquids as they might be a key to understanding predictions from quantum electrodynamics of a “deconfined” state of matter, one where elementary particles split from a conventional description of particles or fields. And yet neither community knows whether this phase even exists. Here, we use computer simulations to provide, for the first time, concrete evidence of its existence.

The emergence of a U(1) Dirac spin liquid (or deconfined matter, in the parlance of high-energy physics) depends on two ingredients: a U(1) gauge field and a spinon. A spinon is a “fractional” spin of a fermion, whereas the U(1) gauge field mediates interactions between spinons. It is thought that a spin liquid arises when spinons and their gauge field are put on a 2D square lattice. To explore this possibility, we design a model by discretizing U(1) gauge fields into a space-time lattice that interacts with fermions.

Using quantum Monte Carlo methods, we simulate the model with various fermion species and find, in all cases, a smoking-gun signature of 2D U(1) deconfined matter. By tuning coupling constants in the model, we also observe continuous transitions between deconfined and confined states. One fermion species also exhibits a novel type of quantum critical point.

We hope that the richness of the phase diagram and firm existence of the U(1) deconfined state of matter will trigger a number of future investigations on the numerical and analytical fronts in the condensed-matter and high-energy communities.