We investigate the ground state phase diagram of an SU(
N)-symmetric antiferromagnetic spin model on a square lattice where each site hosts an irreducible representation of SU(
N) described by a square Young tableau of
N/2 rows and
2S columns. We show that negative sign free fermion Monte Carlo simulations can be carried out for this class of quantum magnets at any
S and even values of
N. In the large-
N limit, the saddle point approximation favors a four-fold degenerate valence bond solid phase. In the large
S-limit, the semi-classical approximation points to Néel state. On a line set by
N=8S+2 in the
S versus
N phase diagram, we observe a variety of phases proximate to the Néel state. At
S=1/2 and
3/2 we observe the aforementioned four fold degenerate valence bond solid state. At
S=1 a two fold degenerate spin nematic state in which the C
4 lattice symmetry is broken down to C
2 emerges. Finally at
S=2 we observe a unique ground state that pertains to a two-dimensional version of the Affleck-Kennedy-Lieb-Tasaki state. For our specific realization, this symmetry protected topological state is characterized by an SU(18),
S=1/2 boundary state, that has a dimerized ground state. These phases that are proximate to the Néel state are consistent with the notion of monopole condensation of the antiferromagnetic order parameter. In particular one expects spin disordered states with degeneracy set by
mod(4,2S).
We consider bipartite
SU(N) spin Hamiltonians with a fundamental representation on one sublattice and a conjugate to fundamental on the other sublattice. By mapping these antiferromagnets to certain classical loop models in one higher dimension, we provide a practical strategy to write down a large family of
SU(N) symmetric spin Hamiltonians that satisfy Marshall's sign condition. This family includes all previously known sign-free
SU(N) spin models in this representation and in addition provides a large set of new models that are Marshall positive and can hence be studied efficiently with quantum Monte Carlo methods. As an application of our idea to the square lattice, we show that in addition to Sandvik's
Q term, there is an independent nontrivial four-spin
R term that is sign free. Using numerical simulations, we show how the
R term provides a new route to the study of quantum criticality of N\'eel order.
The local
ZN quantized Berry phase for the
SU(N) antiferromagnetic Heisenberg spin model is formulated. This quantity, which is a generalization of the local
Z2 Berry phase for SU(2) symmetry, has a direct correspondence to the number of singlet pairs spanning a particular bond, and is effective as a tool to characterize and classify the various symmetry-protected topological phases of one-dimensional
SU(N) spin systems. We extend the path-integral quantum Monte Carlo method for the
Z2 Berry phase in order to calculate the
ZN Berry phase numerically. We demonstrate our method by calculating the
Z4 Berry phase for the bond-alternating
SU(4) antiferromagnetic Heisenberg chain, which is represented by the Young diagram of four columns.
SU ( N ) quantum spin systems may be realized in a variety of physical systems including ultracold atoms in optical lattices. The study of such models also leads to insights into possible novel quantum phases and phase transitions of SU (2) spin models. Here we use Gutzwiller projected fermionic variational wavefunctions to explore the phase diagram and correlation functions of SU ( N ) quantum spin models in the self-conjugate representation. In one dimension, the ground state of the SU (4) spin chain with Heisenberg bilinear and biquadratic interactions is studied by examining instabilities of the Gutzwiller projected free fermion ground state to various broken symmetries. The variational phase diagram so obtained agrees well with exact results. The spin–spin and dimer–dimer correlation functions of the Gutzwiller projected free fermion state with N flavours of fermions are in good agreement with exact and 1/ N calculations for the critical points of SU ( N ) spin chains. In two dimensions, the phase diagram of the antiferromagnetic Heisenberg model on the square lattice is obtained by finding instabilities of the Gutzwiller projected π-flux state. In the absence of biquadratic interactions, the model exhibits long-range Néel order for N = 2 and 4, and spin Peierls (columnar dimer) order for N >4. Upon including biquadratic interactions in the SU (4) model (with a sign appropriate to a fermionic Hubbard model), the Néel order diminishes and eventually disappears, giving way to an extended valence bond crystal. In the case of the SU (6) model, the dimerized ground state melts at sufficiently large biquadratic interaction, yielding a projected π-flux spin liquid phase which in turn undergoes a transition into an extended valence bond crystal at even larger biquadratic interaction. The spin correlations of the projected π-flux state at N = 4 are in good agreement with 1/ N calculations. We find that the state shows strongly enhanced dimer correlations, in qualitative agreement with recent theoretical predictions. We also compare our results with a recent quantum Monte Carlo study of the SU (4) Heisenberg model.
We present a detailed study of the destruction of SU(
N) magnetic order in square lattice bilayer antiferromagnets using unbiased quantum Monte Carlo numerical simulations and field theoretic techniques. We study phase transitions from an SU(
N) N\'eel state into two distinct quantum disordered ``valence-bond'' phases: a valence-bond liquid (VBL) with no broken symmetries and a lattice-symmetry-breaking valence-bond solid (VBS) state. For finite interlayer coupling, the cancellation of Berry phases between the layers has dramatic consequences on the two phase transitions: the N\'eel-VBS transition is first order for all $N\ensuremath{\ge}5$ accesible in our model, whereas the N\'eel-VBL transition is continuous for
N=2 and first order for $N\ensuremath{\ge}4$; for
N=3 the N\'eel-VBL transition show no signs of first-order behavior.
Inspired by our recent works on SU(2) and SU(4) Dirac fermions subjected to plaquette interactions on square lattice, here we extend the large-scale quantum Monte Carlo investigations to the phase diagram of correlated Dirac fermions with SU(6) and SU(8) symmetries subjected to the plaquette interaction on the same lattice. From SU(2) to SU(8), the rich phase diagram exhibits a plethora of emerging quantum phases, such as Dirac semimetals, antiferromagnetic Mott insulators, valence bond solids (VBSs), and Dirac spin liquid and phase transitions, including Gross-Neveu chiral transitions with emergent continuous symmetry, deconfined quantum criticality, and the first-order transition between an interaction-driven columnar VBS and a plaquette VBS. These rich phenomena coming from simple-looking lattice models firmly convey the message that the interplay between the
SU(N) Dirac fermions (with enhanced internal symmetries) and extended plaquette interactions (beyond the on-site Hubbard type) is the new playground to synthesize novel highly entangled quantum matter both at the model level and with experimental feasibilities.