My new paper, *Bose-Einstein condensation of deconfined spinons in two dimensions*, is finally live on arXiv! (arXiv:1909.01594)

## Context

Almost all phase transitions are described by a theory known as the Landau-Ginzburg-Wilson (LGW) paradigm, which describes the phase transition in terms of an order parameter that also describes the ordered state (e.g. a transition to a ferromagnet is described by the magnetization). There is therefore great interest in find examples of phase transitions that do not obey this paradigm. Growing numerical evidence suggests that the transition between the Néel antiferromagnet (AFM) and valence-bond solid (VBS) in certain quantum magnets may be such a transition. Since the Néel AFM and VBS break unrelated symmetries (SU(2) and Z4), LGW predicts the transition between them will be first order. Extensive numerical studies, however, strongly suggest that it is continuous. Instead, this transition appears to be described by *deconfined quantum criticality* (DQC).

In DQC, the critical point is not described by either order parameter, but instead by emergent fractionalized excitations, in this case spinons, which are spin-1/2 *bosons* (crazy, right?). Away from the critical point spinons are confined inside conventional magnon excitations (like quarks in a proton), but at transition they *deconfine*. The existence of deconfined quantum criticality remains controversial.

## In this paper…

… we add a magnetic field to the DQC point to produce a Bose-Einstein condensate (BEC) of magnetic excitations and use thermodynamics to determine if they are spinons or magnons. My collaborators, Harley Scammell and Oleg Sushkov, developed a quantum field theory approach to predict the low-temperature behavior of a spinons in a magnetic field. We found that the field causes the spinon behavior to differ dramatically from magnons. Using my numerics, we show that the magnetic excitations we observe must indeed be bosonic spinons. This constitutes the first evidence for a BEC of spinons and provides more evidence for DQC theory.

## Abstract

The transition between the Néel antiferromagnet and the valence-bond solid state in two dimensions has become a paradigmatic example of deconfined quantum criticality, a non-Landau transition characterized by fractionalized excitations (spinons). We consider an extension of this scenario whereby the deconfined spinons are subject to a magnetic field. The primary purpose is to identify the exotic scenario of a Bose-Einstein condensate of spinons. We employ quantum Monte Carlo simulations of the

J–Qmodel with a magnetic field and perform a quantum field theoretic analysis of the magnetic field and temperature dependence of thermodynamic quantities. The combined analysis provides compelling evidence for the Bose-Einstein condensation of spinons and also demonstrates an extended temperature regime in which the system is best described as gas of spinons interacting with an emergent gauge field.

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