The Rényi entanglement entropy in quantum many-body systems can be viewed as the difference in free energy between partition functions with different trace topologies. We introduce an external field λ that controls the partition function topology, allowing us to define a notion of nonequilibrium work as λ is varied smoothly. Nonequilibrium fluctuation theorems of the work provide us with statistically exact estimates of the Rényi entanglement entropy. This framework also naturally leads to the idea of using quench functions with spatially smooth profiles, providing us a way to average over lattice scale features of the entanglement entropy while preserving long distance universal information. We use these ideas to extract universal information from quantum Monte Carlo simulations of SU(N) spin models in one and two dimensions. The vast gain in efficiency of this method allows us to access unprecedented system sizes up to 192 x 96 spins for the square lattice Heisenberg antiferromagnet.

We consider the easy-plane limit of bipartite SU(N ) Heisenberg Hamiltonians which have a fundamental representation on one sublattice and the conjugate to fundamental on the other sublattice. For N = 2 the easy plane limit of the SU(2) Heisenberg model is the well known quantum XY model of a lattice superfluid. We introduce a logical method to generalize the quantum XY model to arbitrary N , which keeps the Hamiltonian sign-free. We show that these quantum Hamiltonians have a world-line representation as the statistical mechanics of certain tightly packed loop models of N -colors in which neighboring loops are disallowed from having the same color. In this loop representation we design an efficient Monte Carlo cluster algorithm for our model. We present extensive numerical results for these models on the two dimensional square lattice, where we find the nearest neighbor model has superfluid order for N ≤ 5 and valence-bond order for N > 5. By introducing SU(N ) easy-plane symmetric four-spin couplings we are able to tune across the superfluid-VBS phase boundary for all N ≤ 5. We present clear evidence that this quantum phase transition is first order for N = 2 and N = 5, suggesting that easy-plane deconfined criticality runs away generically to a first order transition for small-N .

We study fixed points of the easy-plane CP N −1 field theory by combining quantum Monte Carlo simulations of lattice models of easy-plane SU(N ) superfluids with field theoretic renormalization group calculations, by using ideas of deconfined criticality. From our simulations, we present evidence that at small N our lattice model has a first order phase transition which progressively weakens as N increases, eventually becoming continuous for large values of N . Renormalization group calculations in 4 − dimensions provide an explanation of these results as arising due to the existence of an Nep that separates the fate of the flows with easy-plane anisotropy. When N < Nep the renormalization group flows to a discontinuity fixed point and hence a first order transition arises. On the other hand, for N > Nep the flows are to a new easy-plane CP N −1 fixed point that describes the quantum criticality in the lattice model at large N . Our lattice model at its critical point, thus gives efficient numerical access to a new strongly coupled gauge-matter field theory.Introduction: The study of anti-ferromagnets has uncovered fascinating connections between quantum spin models and gauge theories. The connections have allowed novel gauge theoretic concepts such as deconfinement to be brought into the realm of condensed matter physics. Turning this mapping around, can the study of magnetism provide non-perturbative insights into gauge theories? Remarkably, advances in simulation algorithms for quantum anti-ferromagnets [1] have recently allowed controlled numerical access to otherwise poorly understood strongly coupled gauge theories; the most prominent example being the CP N −1 gauge theory proposed for deconfined critical points (DCP) in SU(N ) magnets [2].In early work on DCP, a prominent role was played by the "easy-plane SU(2)" [3] magnet and its corresponding "easy-plane CP 1 " field theory [2,4]. A self-duality in the field theory suggested that this could be the best candidate for a deconfined critical point [5]. Subsequent numerical work has concluded however that this transition is first order, both in direct discretizations of the field theory [6,7] as well as in simulations of the quantum anti-ferromagnet [8]. The easy-plane case is in contrast to the symmetric SU(N ) case (we refer to this as s-SU(N )), where striking agreement between technical field theoretic calculations [9][10][11][12] and numerical simulations of the quantum magnets has been demonstrated [13][14][15].The sharp contrast between the easy-plane and symmetric cases has been unexplained so far. In this work we address the first order transition in the easy-plane case using both lattice simulations of an ep-SU(N ) model as well as renormalization group calculations on a proposed ep-CP N −1 field theory. We find the first order transition in the ep-SU(N ) models found for N = 2 in previous work persists for larger N . A careful analysis however shows that the first order jump quantitatively weakens as N increases. Renormalization group -expansion ...

We present a study of the scaling behavior of the Rényi entanglement entropy (REE) in SU(N ) spin chain Hamiltonians, in which all of the spins transform under the fundamental representation. These SU(N ) spin chains are known to be quantum critical and described by a well known WessZumino-Witten (WZW) non-linear sigma model in the continuum limit. Numerical results from our lattice Hamiltonian are obtained using stochastic series expansion (SSE) quantum Monte Carlo for both closed and open boundary conditions. As expected for this 1D critical system, the REE shows a logarithmic dependence on the subsystem size with a prefactor given by the central charge of the SU(N ) WZW model. We study in detail the sub-leading oscillatory terms in the REE under both periodic and open boundaries. Each oscillatory term is associated with a WZW field and decays as a power law with an exponent proportional to the scaling dimension of the corresponding field. We find that the use of periodic boundaries (where oscillations are less prominent) allows for a better estimate of the central charge, while using open boundaries allows for a better estimate of the scaling dimensions. We also present numerical data on the thermal Rényi entropy which equally allows for extraction of the central charge.

Building on a recent investigation of the Shastry-Sutherland model [S. Wessel et al., Phys. Rev. B 98, 174432 (2018)], we develop a general strategy to eliminate the Monte Carlo sign problem near the zero-temperature limit in frustrated quantum spin models. If the Hamiltonian of interest and the sign-problem-free Hamiltonian, obtained by making all off-diagonal elements negative in a given basis, have the same ground state and this state is a member of the computational basis, then the average sign returns to one as the temperature goes to zero. We illustrate this technique by studying the triangular and kagome lattice Heisenberg antiferrromagnet in a magnetic field above saturation, as well as the Heisenberg antiferromagnet on a modified Husimi cactus in the dimer basis. We also provide detailed Appendices on using linear programming techniques to automatically generate efficient directed loop updates in quantum Monte Carlo simulations.