First-Order Phase Transition in Easy-Plane Quantum Antiferromagnets

Quantum phase transitions in Mott insulators do not fit easily into the Landau-Ginzburg-Wilson paradigm. A recently proposed alternative to it is the so-called deconfined quantum criticality scenario, providing a new paradigm for quantum phase transitions. In this context it has recently been proposed that a second-order phase transition would occur in a two-dimensional spin $1/2$ quantum antiferromagnet in the deep easy-plane limit. A check of this conjecture is important for understanding the phase structure of Mott insulators. To this end we have performed large-scale Monte Carlo simulations on an effective gauge theory for this system, including a Berry-phase term that projects out the $S=1/2$ sector. The result is a first-order phase transition, thus contradicting the conjecture.

Figure 1

Specific heat $M_2$ of Eq. (3) for various system sizes. Panel (a): Without Berry-phase term. The peak develops into a singularity of the $3\mathrm{D}xy$ type. Panel (b): With Berry-phase term. The peak develops into a $\delta$-function singularity with a peak scaling as $L^3$, consistent with a first-order transition. Note the symmetry and asymmetry of the peaks in the right and left panels, respectively. This is to be expected, since the peaks in the right panel originate with the superposition of a $3\mathrm{D}xy$ peak and an inverted $3\mathrm{D}xy$ peak.

Figure 2

Scaling of the height [panel (a)] and width [panel (b)] of $M_3$ of the action in Eqs. (2, 3). The lines in panel (a) represent $L^{1.43}$ and $L^6$. The former is the $3\mathrm{D}xy$ result. The lines in panel (b) represent $L^{-1.49}$ and $L^{-3}$. The former is the $3\mathrm{D}xy$ result. For large system sizes, the height and width scale in manner consistent with a first-order phase transition. Also shown are results for Eq. (3) with no Berry-phase term $\mathbf{f}=0$ (green symbols). These results follow the $3\mathrm{D}xy$ scaling lines. The red symbols are the results for Eq. (3) while the blue symbols are results for Eq. (2).

Figure 3

Histograms for the probability distribution $P(S,L)$ as a function of $S/L^3$ for various system sizes $L$. (a): results for Eq. (1) in the representation Eq. (3). (b): results Eq. (2). A double-peak structure develops with the latent heat per unit volume approaching a finite constant as $L$ is increased. This is a hallmark of a first-order transition. For the largest systems, up to $120\times {10}^6$ sweeps over the lattice were performed. A total of approximately 500 000 CPU hours were used to obtain these results.

Figure 4

Panel (a) shows the scaling of the height $\Delta F$ of the peak between the two minima in $-\ln P(S,L)$ both for Eqs. (3) (red curve) and (2) (blue curve). Dotted line is the line $\sim L^2$. The height scales as $\Delta F\sim L^{d-1}$. This is a hallmark of a first-order transition. Panel (b) shows latent heat per unit volume $\Delta S/V$ as a function of $L$. The upper (blue) curve is from Eq. (2), the lower (red) curve is from Eq. (3). $\Delta S/V$ approaches a nonzero value as $L$ is increased.