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

arXiv:1110.1183 · Physical Review B

Time-reversal symmetry breaking superconducting ground state in the doped Mott insulator on the honeycomb lattice

Zheng‐Cheng Gu, Hong‐Chen Jiang, D. N. Sheng, Hong Yao, Leon Balents, Xiao-Gang Wen

Published Oct 11, 2013• 74 citations
arXivHTMLPDF

Abstract

The emergence of superconductivity in doped Mott insulators has been debated for decades. In this paper, we report the theoretical discovery of a time-reversal symmetry breaking superconducting ground state in the doped Mott insulator (described by the well known $t$-$J$ model) on honeycomb lattice, based on a recently developed variational method: the Grassmann tensor product state approach. As a benchmark, we use exact diagonalization and density-matrix renormalization methods to check our results on small clusters. We find systematic consistency for the ground-state energy as well as other physical quantities, such as the staggered magnetization. At low doping, the superconductivity coexists with antiferromagnetic ordering.

DOI
10.1103/physrevb.88.155112

Related papers

Time reversal symmetry breaking superconductivity in the honeycomb t-J model

Zheng‐Cheng Gu, Hong‐Chen Jiang, D. N. Sheng +3 more

Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA(Dated: October 7, 2011)We report the theoretical discovery of a novel time reversal symmetry breaking superconductingstate in the t-Jmodel on the honeycomb lattice, based on a recently developed variational method- the Grassmann tensor product state approach. As a benchmark, we use exact diagonalization(ED) and density matrix renormalization (DMRG) methods to check our results on small clusters.Remarkably, we nd systematical consistency for the ground state energy as well as other physicalquantities, such as the staggered magnetization. At low doping, the superconductivity coexists withanti-ferromagnetic ordering.

•Oct 6, 2011•0 citations

Competing orders in the honeycomb lattice t−J model

Zheng-Tao Xu, Zheng‐Cheng Gu, Shuo Yang

We study the honeycomb lattice $t\text{\ensuremath{-}}J$ model using the fermionic tensor network approach. By examining the ansatz with various unit cells, we discover several different stripe states with different periods that compete strongly with uniform states. At very small doping $\ensuremath{\delta}<0.05$, we find almost degenerate uniform $d$-wave superconducting ground states coexisting with antiferromagnetic order. While at larger doping $\ensuremath{\delta}>0.05$, the ground state is an approximately half-filled stripe-ordered state, where the stripe period decreases with increasing hole doping $\ensuremath{\delta}$. Furthermore, the stripe states with the lowest variational energy always display ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave pairing symmetry. The similarity between our results and those on the square lattice contributes to a more comprehensive understanding of doped Mott insulators.

arXiv:2208.13681•Physical review. B./Physical review. B•Jul 24, 2023•14 citations

Spin-charge separation and unconventional superconductivity in \textit{t}-\textit{J} model on honeycomb lattice

Jian-Jian Miao, Zheng-Yuan Yue, Zhang, Hao +2 more

The physical nature of doped Mott-insulator has been intensively studied for more than three decades. It is well known that the single band Hubbard model or $t$-$J$ model on the bipartite lattice is the simplest model to describe a doped Mott insulator. Unfortunately, the key mechanism of superconductivity in these toy models is still under debate. In this paper, we propose a new mechanism for the $d+id$-wave superconductivity (SC) that occurs in the small-doping region of the honeycomb lattice $t$-$J$ model based on the Grassmann tensor product state numerical simulation and spin-charge separation formulation. Moreover, in the presence of anti-ferromagnetic order, a continuum effective field theory for holons is developed near half-filling. It reveals the competition between repulsive and attractive holon interactions induced by spinon fluctuations and gauge fluctuations, respectively. At a large value of $t/J$, the repulsive interaction dominates, leading to the non-Fermi liquid like behavior; while in a moderate range of $t/J$, the attractive interaction dominates, leading to the SC order. Possible experimental detection of spin-charge separation phenomena is also discussed.

arXiv:2301.02274•Jan 5, 2023•0 citations

Correlated Dirac particles and superconductivity on the honeycomb lattice

Wéi Wú, Michael M. Scherer, Carsten Honerkamp A +1 more

We investigate the properties of the nearest-neighbor singlet pairing and the emergence of $d$-wave superconductivity in the doped honeycomb lattice considering the limit of large interactions and the $t\ensuremath{-}{J}_{1}\ensuremath{-}{J}_{2}$ model. First, by applying a renormalized mean-field procedure as well as slave-boson theories which account for the proximity to the Mott-insulating state, we confirm the emergence of $d$-wave superconductivity, in agreement with earlier works. We show that a small but finite ${J}_{2}$ spin coupling between next-nearest neighbors stabilizes $d$-wave symmetry compared to the extended$s$-wave scenario. At small hole doping, to minimize the energy and to gap the whole Fermi surface or all the Dirac points, the superconducting ground state is characterized by a $d+id$ singlet pairing assigned to one valley and a $d\ensuremath{-}id$ singlet pairing to the other, which then preserves time-reversal symmetry. The slightly doped situation is distinct from the heavily doped case (around 3/8 and 5/8 filling) supporting a pure chiral $d+id$ symmetry and breaking time-reversal symmetry. Then, we apply the functional renormalization group and study in more detail the competition between antiferromagnetism and superconductivity in the vicinity of half filling. We discuss possible applications to strongly correlated compounds with copper hexagonal planes such as In${}_{3}$Cu${}_{2}$VO${}_{9}$. Our findings are also relevant to the understanding of exotic superfluidity with cold atoms.

arXiv:1301.1267•Physical Review B•Mar 29, 2013•60 citations

Stripes versus superconductivity in the doped Hubbard model on the honeycomb lattice

Mingpu Qin

We study the ground state of the doped Hubbard model on the honeycomb lattice in the small-doping and strongly interacting region. The nature of the ground state after doping holes into antiferromagnetic Mott insulating states on the honeycomb lattice remains a long-standing unsolved issue, even though tremendous effort has been spent investigating this challenging problem. In this work, we employ two complementary, state-of-the-art, many-body computational methods: constrained path (CP) auxiliary-field quantum Monte Carlo (AFQMC) with self-consistent constraint and density matrix renormalization group (DMRG) methods. Systematic and detailed cross validations are performed between these two methods for narrow systems for which DMRG can produce reliable results. AFQMC is then utilized to study wider systems to investigate the thermodynamic limit properties. The ground state is found to be a half-filled stripe state in the small-doping and strongly interacting region. The pairing correlation shows $d$-wave symmetry locally but decays exponentially with the distance between two pairs.

arXiv:2104.14160•Physical review. B./Physical review. B•Jan 7, 2022•11 citations

Spin-charge separation and unconventional superconductivity in the t − J model on the honeycomb lattice

Jian-Jian Miao, Zheng-Yuan Yue, Hao Zhang +2 more

The physical nature of doped Mott insulators has been the subject of intensive study for decades. The single-band Hubbard model and the $t\text{\ensuremath{-}}J$ model on a bipartite lattice are widely recognized as the simplest models to describe these materials. However, the key mechanism of superconductivity in these toy models remains unclear. Here we propose a novel mechanism for the ($d+id$)-wave superconductivity (SC) that occurs in the small-doping region of the honeycomb lattice $t\text{\ensuremath{-}}J$ model based on the Grassmann tensor product state numerical simulation and spin-charge separation formulation. In the presence of anti-ferromagnetic order near half-filling, we develop a continuum effective field theory for holons, which reveals the competition between repulsive and attractive holon interactions induced by spinon fluctuations and gauge fluctuations, respectively. When $t/J$ is large, the repulsive interaction dominates, leading to a non-Fermi liquid behavior; while in a moderate range of $t/J$, the attractive interaction dominates, leading to the SC order. Potential theoretical and experimental methods to validate the mechanism are discussed.

Physical review. B./Physical review. B•May 14, 2025•1 citation
The emergence of superconductivity in doped Mott insulators has been debated for decades. In this paper, we report the theoretical discovery of a time-reversal symmetry breaking superconducting ground state in the doped Mott insulator (described by the well known ttt-JJJ model) on honeycomb lattice, based on a recently developed variational method: the Grassmann tensor product state approach. As a benchmark, we use exact diagonalization and density-matrix renormalization methods to check our results on small clusters. We find systematic consistency for the ground-state energy as well as other physical quantities, such as the staggered magnetization. At low doping, the superconductivity coexists with antiferromagnetic ordering.
Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA(Dated: October 7, 2011)We report the theoretical discovery of a novel time reversal symmetry breaking superconductingstate in the t-Jmodel on the honeycomb lattice, based on a recently developed variational method- the Grassmann tensor product state approach. As a benchmark, we use exact diagonalization(ED) and density matrix renormalization (DMRG) methods to check our results on small clusters.Remarkably, we nd systematical consistency for the ground state energy as well as other physicalquantities, such as the staggered magnetization. At low doping, the superconductivity coexists withanti-ferromagnetic ordering.
We study the honeycomb lattice $t\text{\ensuremath{-}}J$ model using the fermionic tensor network approach. By examining the ansatz with various unit cells, we discover several different stripe states with different periods that compete strongly with uniform states. At very small doping $\ensuremath{\delta}<0.05$, we find almost degenerate uniform ddd-wave superconducting ground states coexisting with antiferromagnetic order. While at larger doping $\ensuremath{\delta}>0.05$, the ground state is an approximately half-filled stripe-ordered state, where the stripe period decreases with increasing hole doping $\ensuremath{\delta}$. Furthermore, the stripe states with the lowest variational energy always display ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave pairing symmetry. The similarity between our results and those on the square lattice contributes to a more comprehensive understanding of doped Mott insulators.
The physical nature of doped Mott-insulator has been intensively studied for more than three decades. It is well known that the single band Hubbard model or ttt-JJJ model on the bipartite lattice is the simplest model to describe a doped Mott insulator. Unfortunately, the key mechanism of superconductivity in these toy models is still under debate. In this paper, we propose a new mechanism for the d+idd+idd+id-wave superconductivity (SC) that occurs in the small-doping region of the honeycomb lattice ttt-JJJ model based on the Grassmann tensor product state numerical simulation and spin-charge separation formulation. Moreover, in the presence of anti-ferromagnetic order, a continuum effective field theory for holons is developed near half-filling. It reveals the competition between repulsive and attractive holon interactions induced by spinon fluctuations and gauge fluctuations, respectively. At a large value of t/Jt/Jt/J, the repulsive interaction dominates, leading to the non-Fermi liquid like behavior; while in a moderate range of t/Jt/Jt/J, the attractive interaction dominates, leading to the SC order. Possible experimental detection of spin-charge separation phenomena is also discussed.
We investigate the properties of the nearest-neighbor singlet pairing and the emergence of ddd-wave superconductivity in the doped honeycomb lattice considering the limit of large interactions and the $t\ensuremath{-}{J}_{1}\ensuremath{-}{J}_{2}$ model. First, by applying a renormalized mean-field procedure as well as slave-boson theories which account for the proximity to the Mott-insulating state, we confirm the emergence of ddd-wave superconductivity, in agreement with earlier works. We show that a small but finite J2{J}_{2}J2​ spin coupling between next-nearest neighbors stabilizes ddd-wave symmetry compared to the extendedsss-wave scenario. At small hole doping, to minimize the energy and to gap the whole Fermi surface or all the Dirac points, the superconducting ground state is characterized by a d+idd+idd+id singlet pairing assigned to one valley and a $d\ensuremath{-}id$ singlet pairing to the other, which then preserves time-reversal symmetry. The slightly doped situation is distinct from the heavily doped case (around 3/8 and 5/8 filling) supporting a pure chiral d+idd+idd+id symmetry and breaking time-reversal symmetry. Then, we apply the functional renormalization group and study in more detail the competition between antiferromagnetism and superconductivity in the vicinity of half filling. We discuss possible applications to strongly correlated compounds with copper hexagonal planes such as In3{}_{3}3​Cu2{}_{2}2​VO9{}_{9}9​. Our findings are also relevant to the understanding of exotic superfluidity with cold atoms.
We study the ground state of the doped Hubbard model on the honeycomb lattice in the small-doping and strongly interacting region. The nature of the ground state after doping holes into antiferromagnetic Mott insulating states on the honeycomb lattice remains a long-standing unsolved issue, even though tremendous effort has been spent investigating this challenging problem. In this work, we employ two complementary, state-of-the-art, many-body computational methods: constrained path (CP) auxiliary-field quantum Monte Carlo (AFQMC) with self-consistent constraint and density matrix renormalization group (DMRG) methods. Systematic and detailed cross validations are performed between these two methods for narrow systems for which DMRG can produce reliable results. AFQMC is then utilized to study wider systems to investigate the thermodynamic limit properties. The ground state is found to be a half-filled stripe state in the small-doping and strongly interacting region. The pairing correlation shows ddd-wave symmetry locally but decays exponentially with the distance between two pairs.
The physical nature of doped Mott insulators has been the subject of intensive study for decades. The single-band Hubbard model and the $t\text{\ensuremath{-}}J$ model on a bipartite lattice are widely recognized as the simplest models to describe these materials. However, the key mechanism of superconductivity in these toy models remains unclear. Here we propose a novel mechanism for the (d+idd+idd+id)-wave superconductivity (SC) that occurs in the small-doping region of the honeycomb lattice $t\text{\ensuremath{-}}J$ model based on the Grassmann tensor product state numerical simulation and spin-charge separation formulation. In the presence of anti-ferromagnetic order near half-filling, we develop a continuum effective field theory for holons, which reveals the competition between repulsive and attractive holon interactions induced by spinon fluctuations and gauge fluctuations, respectively. When t/Jt/Jt/J is large, the repulsive interaction dominates, leading to a non-Fermi liquid behavior; while in a moderate range of t/Jt/Jt/J, the attractive interaction dominates, leading to the SC order. Potential theoretical and experimental methods to validate the mechanism are discussed.