Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Conference on Symmetry (Symmetry)

Quantum Simulation of SU(4) Symmetric Spin Lattice Models

Bruno Uchoa

Published Jan 8, 2018• 0 citations
Publisher

Abstract

first_page settings Order Article Reprints Font Type: Arial Georgia Verdana Font Size: Aa Aa Aa Line Spacing:    Column Width:    Background: Open AccessAbstract Quantum Simulation of SU(4) Symmetric Spin Lattice Models † by Bruno Uchoa Department of Physics and Astronomy, University of Oklahoma, Norman, OK 73019, USA † Presented at Symmetry 2017—The First International Conference on Symmetry, Barcelona, Spain, 16–18 October 2017. Proceedings 2018, 2(1), 39; https://doi.org/10.3390/proceedings2010039 Published: 8 January 2018 (This article belongs to the Proceedings of The First International Conference on Symmetry) Download Download PDF Download PDF with Cover Download XML Versions Notes Quantum spin-orbital liquids are strongly correlated states that emerge from quantum frustration between spin and orbital degrees of freedom. Those states are highly entangled, have non-local excitations but do not break any symmetries. A promising route towards observing those elusive states is the creation of artificial Mott insulators, where antiferromagnetic correlations between spins and orbitals can be designed. I will show that Coulomb impurity lattices on the surface of gapped honeycomb substrates, such as graphene on SiC, can be used to simulate SU(4) symmetric spin-orbital lattice models in the Mott regime. The antiferromagnetic correlations follow from super-exchange interactions between Coulomb impurity bound states at quarter filling, with spin and valley degeneracies. I propose that quantum spin-orbital liquids can be engineered in artificially designed solid-state systems at vastly higher temperatures than achievable in optical lattices with cold atoms. © 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Share and Cite MDPI and ACS Style Uchoa, B. Quantum Simulation of SU(4) Symmetric Spin Lattice Models. Proceedings 2018, 2, 39. https://doi.org/10.3390/proceedings2010039 AMA Style Uchoa B. Quantum Simulation of SU(4) Symmetric Spin Lattice Models. Proceedings. 2018; 2(1):39. https://doi.org/10.3390/proceedings2010039 Chicago/Turabian Style Uchoa, Bruno. 2018. "Quantum Simulation of SU(4) Symmetric Spin Lattice Models" Proceedings 2, no. 1: 39. https://doi.org/10.3390/proceedings2010039 Find Other Styles Article Metrics No No Article Access Statistics Multiple requests from the same IP address are counted as one view.

DOI
10.3390/proceedings2010039

Related papers

PhD Thesis: Searching for an emergent SU(4) symmetry in real materials

Masahiko G. Yamada

The enhancement of the spin-space symmetry from the usual $\mathrm{SU}(2)$ to $\mathrm{SU}(N)$ with $N>2$ is promising for finding nontrivial quantum spin liquids, but the realization of $\mathrm{SU}(N)$ spin systems in real materials is still challenging. Although there is a proposal in cold atomic systems, in magnetic materials with a spin-orbital degree of freedom it is difficult to achieve the $\mathrm{SU}(N)$ symmetry by fine tuning. Here we propose a new mechanism by which the $\mathrm{SU}(4)$ symmetry emerges in the strong spin-orbit coupling limit. In $d^1$ transition metal compounds with edge-sharing anion octahedra, the spin-orbit coupling gives rise to strongly bond-dependent and apparently $\mathrm{SU}(4)$-breaking hopping between the $J_\textrm{eff}=3/2$ quartets. However, in the honeycomb structure, a gauge transformation maps the system to an $\mathrm{SU}(4)$-symmetric Hubbard model, which means that the system has a hidden symmetry in spite of its large spin-orbit coupling. In the strong repulsion limit at quarter filling, as expected in $α$-ZrCl$_3,$ the low-energy effective model is the $\mathrm{SU}(4)$ Heisenberg model on the honeycomb lattice, which cannot have a trivial gapped ground state and is expected to host a gapless spin-orbital liquid. In such quantum spin-orbital liquids, both the spin and orbital degrees of freedom become fractionalized and correlated together at low temperature due to the strong frustrated interactions between them. Similarly to spinons in pure quantum spin liquids, quantum spin-orbital liquids can host not only spinon excitations, but also fermionic "orbitalon" excitations at low temperature, which we have named here in distinction from orbitons in the symmetry-broken Jahn-Teller phases.

arXiv:2004.01716•Apr 3, 2020•0 citations

SU(4)-symmetric quantum spin-orbital liquids on various lattices

Masahiko G. Yamada, Masaki Oshikawa, George Jackeli

An emergent SU(4) symmetry discovered in the microscopic model for d1 honeycomb materials [M. G. Yamada, M. Oshikawa, and G. Jackeli, ] has enabled us to tailor exotic SU(4) models in real materials. In the honeycomb structure, the emergent SU(4) Heisenberg model would potentially have a quantum spin-orbital liquid ground state due to the , and we can also expect similar spin-orbital liquids in three-dimensional versions of the honeycomb lattice. In such quantum spin-orbital liquids, both the spin and orbital degrees of freedom become fractionalized and entangled together due to the strong frustrated interactions between them. Similarly to spinons in pure quantum spin liquids, quantum spin-orbital liquids can host not only spinon excitations, but also fermionic excitations at low temperature.

arXiv:2103.17076•Physical review. B./Physical review. B•Dec 30, 2021•17 citations

SU(4) Heisenberg model on the honeycomb lattice with exchange-frustrated perturbations: Implications for twistronics and Mott insulators

W. M. H. Natori, Rajah P. Nutakki, Rodrigo G. Pereira +1 more

The SU(4)-symmetric spin-orbital model on the honeycomb lattice was recently studied in connection to correlated insulators such as the ${e}_{g}$ Mott insulator ${\mathrm{Ba}}_{3}{\mathrm{CuSb}}_{2}{\mathrm{O}}_{9}$ and the insulating phase of magic-angle twisted bilayer graphene at quarter filling. Here we provide a unified discussion of these systems by investigating an extended model that includes the effects of Hund's coupling and anisotropic, orbital-dependent exchange interactions. Using a combination of mean-field theory, linear flavor-wave theory, and variational Monte Carlo, we show that this model harbors a quantum spin-orbital liquid over a wide parameter regime around the SU(4)-symmetric point. For large Hund's coupling, a ferromagnetic antiferro-orbital ordered state appears, while a valence-bond crystal combined with a vortex orbital state is stabilized by dominant orbital-dependent exchange interactions.

arXiv:1908.09224•Physical review. B./Physical review. B•Nov 21, 2019•43 citations

Emergent SU ( 4 ) Symmetry in α − ZrCl 3 and Crystalline Spin-Orbital Liquids

Masahiko G. Yamada, Masaki Oshikawa, George Jackeli

While the enhancement of spin-space symmetry from the usual SU(2) to SU(N) is promising for finding nontrivial quantum spin liquids, its realization in magnetic materials remains challenging. Here, we propose a new mechanism by which SU(4) symmetry emerges in the strong spin-orbit coupling limit. In d^{1} transition metal compounds with edge-sharing anion octahedra, the spin-orbit coupling gives rise to strongly bond-dependent and apparently SU(4)-breaking hopping between the J_{eff}=3/2 quartets. However, in the honeycomb structure, a gauge transformation maps the system to an SU(4)-symmetric Hubbard model. In the strong repulsion limit at quarter filling, as realized in α-ZrCl_{3}, the low-energy effective model is the SU(4) Heisenberg model on the honeycomb lattice, which cannot have a trivial gapped ground state and is expected to host a gapless spin-orbital liquid. By generalizing this model to other three-dimensional lattices, we also propose crystalline spin-orbital liquids protected by this emergent SU(4) symmetry and space group symmetries.

arXiv:1709.05252•Physical Review Letters•Aug 27, 2018•88 citations

Theory of Dirac Spin-Orbital Liquids: monopoles, anomalies, and applications to $SU(4)$ honeycomb models

Vladimir Calvera, Wang, Chong

Dirac spin liquids represent a class of highly-entangled quantum phases in two dimensional Mott insulators, featuring exotic properties such as critical correlation functions and absence of well-defined low energy quasi-particles. Existing numerical works suggest that the spin-orbital $SU(4)$ symmetric Kugel-Khomskii model of Mott insulators on the honeycomb lattice realizes a Dirac spin-orbital liquid, described at low energy by $(2+1)d$ quantum electrodynamics (QED$_3$) with $N_f=8$ Dirac fermions. We generalize methods previously developed for $SU(2)$ spin systems to analyze the symmetry properties and stability of the Dirac spin-orbital liquid. We conclude that the standard Dirac state in the $SU(4)$ honeycomb system, based on a simple parton mean-field ansatz, is intrinsically unstable at low energy due to the existence of a monopole perturbation that is allowed by physical symmetries and relevant under renormalization group flow. We propose two plausible alternative scenarios compatible with existing numerics. In the first scenario, we propose an alternative $U(1)$ Dirac spin-orbital liquid, which is similar to the standard one except for its monopole symmetry quantum numbers. This alternative $U(1)$ state represents a stable gapless phase. In the second scenario, we start from the standard $U(1)$ Dirac liquid and Higgs the $U(1)$ gauge symmetry down to $\mathbb{Z}_4$. The resulting $\mathbb{Z}_4$ Dirac spin-orbital liquid is stable. We also discuss the continuous quantum phase transitions from the $\mathbb{Z}_4$ Dirac liquids to conventional symmetry-breaking orders, described by the QED$_3$ theory with $N_f=8$ supplemented with a critical charge-$4$ Higgs field. We discuss possible ways to distinguish these scenarios in numerics. We also extend previous calculations of the quantum anomalies of QED$_3$ and match with generalized lattice Lieb-Schultz-Mattis constraints.

arXiv:2103.13405•Mar 24, 2021•8 citations

Dimer description of the SU(4) antiferromagnet on the triangular lattice

Anna Keselman, L. Savary, Leon Balents

In systems with many local degrees of freedom, high-symmetry points in the phase diagram can provide an important starting point for the investigation of their properties throughout the phase diagram. In systems with both spin and orbital (or valley) degrees of freedom such a starting point gives rise to SU(4)-symmetric models. Here we consider SU(4)-symmetric "spin'' models, corresponding to Mott phases at half-filling, i.e. the six-dimensional representation of SU(4). This may be relevant to twisted multilayer graphene. In particular, we study the SU(4) antiferromagnetic "Heisenberg'' model on the triangular lattice, both in the classical limit and in the quantum regime. Carrying out a numerical study using the density matrix renormalization group (DMRG), we argue that the ground state is non-magnetic. We then derive a dimer expansion of the SU(4) spin model. An exact diagonalization (ED) study of the effective dimer model suggests that the ground state breaks translation invariance, forming a valence bond solid (VBS) with a 12-site unit cell. Finally, we consider the effect of SU(4)-symmetry breaking interactions due to Hund's coupling, and argue for a possible phase transition between a VBS and a magnetically ordered state.

arXiv:1911.03492•SciPost Physics•May 13, 2020•9 citations
first_page settings Order Article Reprints Font Type: Arial Georgia Verdana Font Size: Aa Aa Aa Line Spacing:    Column Width:    Background: Open AccessAbstract Quantum Simulation of SU(4) Symmetric Spin Lattice Models † by Bruno Uchoa Department of Physics and Astronomy, University of Oklahoma, Norman, OK 73019, USA † Presented at Symmetry 2017—The First International Conference on Symmetry, Barcelona, Spain, 16–18 October 2017. Proceedings 2018, 2(1), 39; https://doi.org/10.3390/proceedings2010039 Published: 8 January 2018 (This article belongs to the Proceedings of The First International Conference on Symmetry) Download Download PDF Download PDF with Cover Download XML Versions Notes Quantum spin-orbital liquids are strongly correlated states that emerge from quantum frustration between spin and orbital degrees of freedom. Those states are highly entangled, have non-local excitations but do not break any symmetries. A promising route towards observing those elusive states is the creation of artificial Mott insulators, where antiferromagnetic correlations between spins and orbitals can be designed. I will show that Coulomb impurity lattices on the surface of gapped honeycomb substrates, such as graphene on SiC, can be used to simulate SU(4) symmetric spin-orbital lattice models in the Mott regime. The antiferromagnetic correlations follow from super-exchange interactions between Coulomb impurity bound states at quarter filling, with spin and valley degeneracies. I propose that quantum spin-orbital liquids can be engineered in artificially designed solid-state systems at vastly higher temperatures than achievable in optical lattices with cold atoms. © 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Share and Cite MDPI and ACS Style Uchoa, B. Quantum Simulation of SU(4) Symmetric Spin Lattice Models. Proceedings 2018, 2, 39. https://doi.org/10.3390/proceedings2010039 AMA Style Uchoa B. Quantum Simulation of SU(4) Symmetric Spin Lattice Models. Proceedings. 2018; 2(1):39. https://doi.org/10.3390/proceedings2010039 Chicago/Turabian Style Uchoa, Bruno. 2018. "Quantum Simulation of SU(4) Symmetric Spin Lattice Models" Proceedings 2, no. 1: 39. https://doi.org/10.3390/proceedings2010039 Find Other Styles Article Metrics No No Article Access Statistics Multiple requests from the same IP address are counted as one view.
The enhancement of the spin-space symmetry from the usual SU(2)\mathrm{SU}(2)SU(2) to SU(N)\mathrm{SU}(N)SU(N) with N>2N>2N>2 is promising for finding nontrivial quantum spin liquids, but the realization of SU(N)\mathrm{SU}(N)SU(N) spin systems in real materials is still challenging. Although there is a proposal in cold atomic systems, in magnetic materials with a spin-orbital degree of freedom it is difficult to achieve the SU(N)\mathrm{SU}(N)SU(N) symmetry by fine tuning. Here we propose a new mechanism by which the SU(4)\mathrm{SU}(4)SU(4) symmetry emerges in the strong spin-orbit coupling limit. In d1d^1d1 transition metal compounds with edge-sharing anion octahedra, the spin-orbit coupling gives rise to strongly bond-dependent and apparently SU(4)\mathrm{SU}(4)SU(4)-breaking hopping between the Jeff=3/2J_\textrm{eff}=3/2Jeff​=3/2 quartets. However, in the honeycomb structure, a gauge transformation maps the system to an SU(4)\mathrm{SU}(4)SU(4)-symmetric Hubbard model, which means that the system has a hidden symmetry in spite of its large spin-orbit coupling. In the strong repulsion limit at quarter filling, as expected in ααα-ZrCl3,_3,3​, the low-energy effective model is the SU(4)\mathrm{SU}(4)SU(4) Heisenberg model on the honeycomb lattice, which cannot have a trivial gapped ground state and is expected to host a gapless spin-orbital liquid. In such quantum spin-orbital liquids, both the spin and orbital degrees of freedom become fractionalized and correlated together at low temperature due to the strong frustrated interactions between them. Similarly to spinons in pure quantum spin liquids, quantum spin-orbital liquids can host not only spinon excitations, but also fermionic "orbitalon" excitations at low temperature, which we have named here in distinction from orbitons in the symmetry-broken Jahn-Teller phases.
An emergent SU(4) symmetry discovered in the microscopic model for d1 honeycomb materials [M. G. Yamada, M. Oshikawa, and G. Jackeli, ] has enabled us to tailor exotic SU(4) models in real materials. In the honeycomb structure, the emergent SU(4) Heisenberg model would potentially have a quantum spin-orbital liquid ground state due to the , and we can also expect similar spin-orbital liquids in three-dimensional versions of the honeycomb lattice. In such quantum spin-orbital liquids, both the spin and orbital degrees of freedom become fractionalized and entangled together due to the strong frustrated interactions between them. Similarly to spinons in pure quantum spin liquids, quantum spin-orbital liquids can host not only spinon excitations, but also fermionic excitations at low temperature.
The SU(4)-symmetric spin-orbital model on the honeycomb lattice was recently studied in connection to correlated insulators such as the eg{e}_{g}eg​ Mott insulator Ba3CuSb2O9{\mathrm{Ba}}_{3}{\mathrm{CuSb}}_{2}{\mathrm{O}}_{9}Ba3​CuSb2​O9​ and the insulating phase of magic-angle twisted bilayer graphene at quarter filling. Here we provide a unified discussion of these systems by investigating an extended model that includes the effects of Hund's coupling and anisotropic, orbital-dependent exchange interactions. Using a combination of mean-field theory, linear flavor-wave theory, and variational Monte Carlo, we show that this model harbors a quantum spin-orbital liquid over a wide parameter regime around the SU(4)-symmetric point. For large Hund's coupling, a ferromagnetic antiferro-orbital ordered state appears, while a valence-bond crystal combined with a vortex orbital state is stabilized by dominant orbital-dependent exchange interactions.
While the enhancement of spin-space symmetry from the usual SU(2) to SU(N) is promising for finding nontrivial quantum spin liquids, its realization in magnetic materials remains challenging. Here, we propose a new mechanism by which SU(4) symmetry emerges in the strong spin-orbit coupling limit. In d^{1} transition metal compounds with edge-sharing anion octahedra, the spin-orbit coupling gives rise to strongly bond-dependent and apparently SU(4)-breaking hopping between the J_{eff}=3/2 quartets. However, in the honeycomb structure, a gauge transformation maps the system to an SU(4)-symmetric Hubbard model. In the strong repulsion limit at quarter filling, as realized in α-ZrCl_{3}, the low-energy effective model is the SU(4) Heisenberg model on the honeycomb lattice, which cannot have a trivial gapped ground state and is expected to host a gapless spin-orbital liquid. By generalizing this model to other three-dimensional lattices, we also propose crystalline spin-orbital liquids protected by this emergent SU(4) symmetry and space group symmetries.
Theory of Dirac Spin-Orbital Liquids: monopoles, anomalies, and applications to SU(4)SU(4)SU(4) honeycomb models
Dirac spin liquids represent a class of highly-entangled quantum phases in two dimensional Mott insulators, featuring exotic properties such as critical correlation functions and absence of well-defined low energy quasi-particles. Existing numerical works suggest that the spin-orbital SU(4)SU(4)SU(4) symmetric Kugel-Khomskii model of Mott insulators on the honeycomb lattice realizes a Dirac spin-orbital liquid, described at low energy by (2+1)d(2+1)d(2+1)d quantum electrodynamics (QED3_33​) with Nf=8N_f=8Nf​=8 Dirac fermions. We generalize methods previously developed for SU(2)SU(2)SU(2) spin systems to analyze the symmetry properties and stability of the Dirac spin-orbital liquid. We conclude that the standard Dirac state in the SU(4)SU(4)SU(4) honeycomb system, based on a simple parton mean-field ansatz, is intrinsically unstable at low energy due to the existence of a monopole perturbation that is allowed by physical symmetries and relevant under renormalization group flow. We propose two plausible alternative scenarios compatible with existing numerics. In the first scenario, we propose an alternative U(1)U(1)U(1) Dirac spin-orbital liquid, which is similar to the standard one except for its monopole symmetry quantum numbers. This alternative U(1)U(1)U(1) state represents a stable gapless phase. In the second scenario, we start from the standard U(1)U(1)U(1) Dirac liquid and Higgs the U(1)U(1)U(1) gauge symmetry down to Z4\mathbb{Z}_4Z4​. The resulting Z4\mathbb{Z}_4Z4​ Dirac spin-orbital liquid is stable. We also discuss the continuous quantum phase transitions from the Z4\mathbb{Z}_4Z4​ Dirac liquids to conventional symmetry-breaking orders, described by the QED3_33​ theory with Nf=8N_f=8Nf​=8 supplemented with a critical charge-444 Higgs field. We discuss possible ways to distinguish these scenarios in numerics. We also extend previous calculations of the quantum anomalies of QED3_33​ and match with generalized lattice Lieb-Schultz-Mattis constraints.
In systems with many local degrees of freedom, high-symmetry points in the phase diagram can provide an important starting point for the investigation of their properties throughout the phase diagram. In systems with both spin and orbital (or valley) degrees of freedom such a starting point gives rise to SU(4)-symmetric models. Here we consider SU(4)-symmetric "spin'' models, corresponding to Mott phases at half-filling, i.e. the six-dimensional representation of SU(4). This may be relevant to twisted multilayer graphene. In particular, we study the SU(4) antiferromagnetic "Heisenberg'' model on the triangular lattice, both in the classical limit and in the quantum regime. Carrying out a numerical study using the density matrix renormalization group (DMRG), we argue that the ground state is non-magnetic. We then derive a dimer expansion of the SU(4) spin model. An exact diagonalization (ED) study of the effective dimer model suggests that the ground state breaks translation invariance, forming a valence bond solid (VBS) with a 12-site unit cell. Finally, we consider the effect of SU(4)-symmetry breaking interactions due to Hund's coupling, and argue for a possible phase transition between a VBS and a magnetically ordered state.