Phase diagram of the SU( $N$ ) antiferromagnet of spin $S$ on a square latticePhase diagram of the SU($N$) antiferromagnet of spin $S$ on a square lattice

Jonas Schwab, Francesco Parisen Toldin, Fakher F. Assaad

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 $\text{mod}(4,2S)$ .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 $\text{mod}(4,2S)$.

arXiv:2304.07329Apr 14, 20230 citations

Phase diagram of the SU(N) antiferromagnet of spin S on a square lattice

Jonas Schwab, Francesco Parisen Toldin, Fakher F. Assaad

Spin systems are a fundamental concept in condensed matter and statistical physics. Here, the authors provide the very first computation of the spin- $S$ SU(N) antiferromagnet in a representation amenable to negative sign free fermion Monte Carlo simulations. They offer a numerical proof of the seminal works of Read and Sachdev. It highlights the close connection between topology and the melting of the quantum antiferromagnet, with the Berry phase explaining the various states observed in the vicinity of the quantum antiferromagnet.Spin systems are a fundamental concept in condensed matter and statistical physics. Here, the authors provide the very first computation of the spin-$S$ SU(N) antiferromagnet in a representation amenable to negative sign free fermion Monte Carlo simulations. They offer a numerical proof of the seminal works of Read and Sachdev. It highlights the close connection between topology and the melting of the quantum antiferromagnet, with the Berry phase explaining the various states observed in the vicinity of the quantum antiferromagnet.

Physical review. B./Physical review. BSep 25, 20233 citations

Fate of CPN−1 Fixed Points with q Monopoles

Matthew S. Block, Roger G. Melko, Ribhu K. Kaul

We present an extensive quantum Monte Carlo study of the Néel to valence-bond solid (VBS) phase transition on rectangular- and honeycomb-lattice SU(N) antiferromagnets in sign-problem-free models. We find that in contrast to the honeycomb lattice and previously studied square-lattice systems, on the rectangular lattice for small N, a first-order Néel-VBS transition is realized. On increasing N≥4, we observe that the transition becomes continuous and with the same universal exponents as found on the honeycomb and square lattices (studied here for N=5, 7, 10), providing strong support for a deconfined quantum critical point. Combining our new results with previous numerical and analytical studies, we present a general phase diagram of the stability of CPN-1 fixed points with q monopoles.We present an extensive quantum Monte Carlo study of the Néel to valence-bond solid (VBS) phase transition on rectangular- and honeycomb-lattice SU(N) antiferromagnets in sign-problem-free models. We find that in contrast to the honeycomb lattice and previously studied square-lattice systems, on the rectangular lattice for small N, a first-order Néel-VBS transition is realized. On increasing N≥4, we observe that the transition becomes continuous and with the same universal exponents as found on the honeycomb and square lattices (studied here for N=5, 7, 10), providing strong support for a deconfined quantum critical point. Combining our new results with previous numerical and analytical studies, we present a general phase diagram of the stability of CPN-1 fixed points with q monopoles.

arXiv:1307.0519Physical Review LettersSep 26, 2013121 citations

The phase structure of the SU(2) × SU(2) spin system in two dimensions

Michele Caselle, Ferdinando Gliozzi, R. Megna

Physics Letters BFeb 1, 198218 citations

Phase diagram of the SU(

N

) antiferromagnet of spin

S

on a square lattice

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

\text{mod}(4,2S)

Spin systems are a fundamental concept in condensed matter and statistical physics. Here, the authors provide the very first computation of the spin-

S

SU(N) antiferromagnet in a representation amenable to negative sign free fermion Monte Carlo simulations. They offer a numerical proof of the seminal works of Read and Sachdev. It highlights the close connection between topology and the melting of the quantum antiferromagnet, with the Berry phase explaining the various states observed in the vicinity of the quantum antiferromagnet.