Competition between Neel, Haldane nematic, plaquette valence bond solid, and $(π,π)$ valence bond solid phases in SU(N) analogs of $S=1$ square-lattice antiferromagnets
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| Natura: | Preprint |
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2023
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| author | Kundu, Souvik Desai, Nisheeta Damle, Kedar |
| author_facet | Kundu, Souvik Desai, Nisheeta Damle, Kedar |
| contents | We use stochastic series expansion (SSE) quantum Monte Carlo (QMC) methods to study the phases and transitions displayed by a class of sign-free designer Hamiltonians for SU($N$) analogs of spin $S=1$ quantum antiferromagnets on the square lattice. The SU($N$) spins are generators of the single-row two-column representation (complex conjugate of single-row two-column representation) on $A$ ($B$) sublattices of the square lattice, and the Hamiltonian is designed to explore the competition between the nearest neighbour antiferromagnetic exchange couplings $J$ and four-spin interactions $Q$ that favor a plaquette-ordered valence bond solid (p-VBS) ground state. We find that this state is indeed established at large $Q/J$ for all $N > 3$. For $3< N \leq 9$, the ground state exhibits a direct first order quantum phase transition from a small-$Q/J$ Néel ordered antiferromagnetic state to this large-$Q/J$ p-VBS state. The ground state at $Q/J=0$ for $N \geq 10$ has been previously reported to be a valence bond nematic state, dubbed the Haldane nematic in recent literature. For small nonzero $Q/J$ and $N \geq 10$, we additionally find an unusual intermediate state in which the bond energy has a Bragg peak at wavevector $(π,π)$ with no accompanying Bragg peaks at wavevectors $(π,0)$ and $(0, π)$. This $(π, π)$ state also appears to be metastable at $Q/J =0$, as evidenced by low temperature histograms of the Haldane nematic and $(π, π)$ order parameters. Deep in the p-VBS phase of the ground state phase diagram, we find the temperature-driven melting of the p-VBS order is in the Ashkin-Teller universality class. In this regime, we identify an interesting signature of Ashkin-Teller criticality in bond correlations at wavevector $(π, π)$; this is in addition to the expected critical fluctuations of the conventional p-VBS order parameter at wavevectors $(π,0)$ and $(0,π)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_12262 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Competition between Neel, Haldane nematic, plaquette valence bond solid, and $(π,π)$ valence bond solid phases in SU(N) analogs of $S=1$ square-lattice antiferromagnets Kundu, Souvik Desai, Nisheeta Damle, Kedar Strongly Correlated Electrons We use stochastic series expansion (SSE) quantum Monte Carlo (QMC) methods to study the phases and transitions displayed by a class of sign-free designer Hamiltonians for SU($N$) analogs of spin $S=1$ quantum antiferromagnets on the square lattice. The SU($N$) spins are generators of the single-row two-column representation (complex conjugate of single-row two-column representation) on $A$ ($B$) sublattices of the square lattice, and the Hamiltonian is designed to explore the competition between the nearest neighbour antiferromagnetic exchange couplings $J$ and four-spin interactions $Q$ that favor a plaquette-ordered valence bond solid (p-VBS) ground state. We find that this state is indeed established at large $Q/J$ for all $N > 3$. For $3< N \leq 9$, the ground state exhibits a direct first order quantum phase transition from a small-$Q/J$ Néel ordered antiferromagnetic state to this large-$Q/J$ p-VBS state. The ground state at $Q/J=0$ for $N \geq 10$ has been previously reported to be a valence bond nematic state, dubbed the Haldane nematic in recent literature. For small nonzero $Q/J$ and $N \geq 10$, we additionally find an unusual intermediate state in which the bond energy has a Bragg peak at wavevector $(π,π)$ with no accompanying Bragg peaks at wavevectors $(π,0)$ and $(0, π)$. This $(π, π)$ state also appears to be metastable at $Q/J =0$, as evidenced by low temperature histograms of the Haldane nematic and $(π, π)$ order parameters. Deep in the p-VBS phase of the ground state phase diagram, we find the temperature-driven melting of the p-VBS order is in the Ashkin-Teller universality class. In this regime, we identify an interesting signature of Ashkin-Teller criticality in bond correlations at wavevector $(π, π)$; this is in addition to the expected critical fluctuations of the conventional p-VBS order parameter at wavevectors $(π,0)$ and $(0,π)$. |
| title | Competition between Neel, Haldane nematic, plaquette valence bond solid, and $(π,π)$ valence bond solid phases in SU(N) analogs of $S=1$ square-lattice antiferromagnets |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2309.12262 |