arXiv:2310.02645 · Physical review. B./Physical review. B

Candidate quantum disordered intermediate phase in the Heisenberg antiferromagnet on the maple-leaf lattice

Lasse Gresista, Ciarán Hickey, Simon Trebst, Yasir Iqbal

Published Dec 19, 2023• 22 citations

Abstract

Quantum antiferromagnets on geometrically frustrated lattices have long attracted interest for the formation of quantum disordered states and the possible emergence of quantum spin liquid (QSL) ground states. Here we turn to the nearest-neighbor spin-$1/2$ Heisenberg antiferromagnet on the maple-leaf lattice, which is known to relieve frustration by the formation of canted ${120}^{\ensuremath{\circ}}$ magnetic order or valence bond crystal order when varying the bond anisotropy. Employing a pseudofermion functional renormalization group approach to assess its ground state phase diagram in detail, we present evidence for a QSL regime sandwiched between these two limiting phases. The formation of such a QSL might signal proximity to a possible deconfined quantum critical point from which it emerges, and that is potentially accessible by tuning the exchange couplings. Our conclusions are based on large-scale simulations involving a careful finite-size scaling analysis of the behavior of magnetic susceptibility and spin-spin correlation functions under renormalization group flow.

DOI: 10.1103/physrevb.108.l241116

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Phase diagram of the J − J d Heisenberg model on the maple leaf lattice: Neural networks and density matrix renormalization group

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arXiv:2310.02645 · Physical review. B./Physical review. B

Candidate quantum disordered intermediate phase in the Heisenberg antiferromagnet on the maple-leaf lattice

Lasse Gresista, Ciarán Hickey, Simon Trebst, Yasir Iqbal

Published Dec 19, 2023• 22 citations

arXiv HTML PDF

Abstract

1/2

Heisenberg antiferromagnet on the maple-leaf lattice, which is known to relieve frustration by the formation of canted

{120}^{\ensuremath{\circ}}

magnetic order or valence bond crystal order when varying the bond anisotropy. Employing a pseudofermion functional renormalization group approach to assess its ground state phase diagram in detail, we present evidence for a QSL regime sandwiched between these two limiting phases. The formation of such a QSL might signal proximity to a possible deconfined quantum critical point from which it emerges, and that is potentially accessible by tuning the exchange couplings. Our conclusions are based on large-scale simulations involving a careful finite-size scaling analysis of the behavior of magnetic susceptibility and spin-spin correlation functions under renormalization group flow.

DOI: 10.1103/physrevb.108.l241116

Related papers

Where is the spin liquid in maple-leaf quantum magnet?

Pratyay Ghosh

We investigate the possibility of exotic phenomena, viz. quantum spin liquid (QSL) or deconfined quantum critical point (DQCP), in the spin- $\frac{1}{2}$ Heisenberg model on the maple-leaf lattice, a geometrically frustrated system formed by hexagons (coupling $J_h$ ), triangles (coupling $J_t$ ), and dimers (coupling $J_d$ ). We identify one promising region, given by $J_h > 0$ and $J_t, J_d < 0$ , for hosting enticing physics. In this region, the quantum phase diagram of the system exhibits an interplay between Néel order and a gapped dimerized singlet phase. This arrangement holds the possibility of harboring a QSL and a DQCP. Using bond-operator mean-field theory and density matrix renormalization group calculations, we delve into this uncharted territory, revealing tantalizing evidence of the existence of a QSL phase and highlighting its potential as a platform for DQCP.We investigate the possibility of exotic phenomena, viz. quantum spin liquid (QSL) or deconfined quantum critical point (DQCP), in the spin-$\frac{1}{2}$ Heisenberg model on the maple-leaf lattice, a geometrically frustrated system formed by hexagons (coupling $J_h$), triangles (coupling $J_t$), and dimers (coupling $J_d$). We identify one promising region, given by $J_h > 0$ and $J_t, J_d < 0$, for hosting enticing physics. In this region, the quantum phase diagram of the system exhibits an interplay between Néel order and a gapped dimerized singlet phase. This arrangement holds the possibility of harboring a QSL and a DQCP. Using bond-operator mean-field theory and density matrix renormalization group calculations, we delve into this uncharted territory, revealing tantalizing evidence of the existence of a QSL phase and highlighting its potential as a platform for DQCP.

arXiv:2401.09422Jan 17, 20242 citations

Unconventional orders in the maple-leaf ferro-antiferromagnetic Heisenberg model

Lasse Gresista, Dominik Kiese, Simon Trebst +1 more

Motivated by the search for unconventional orders in frustrated quantum magnets, we present a multi-method investigation into the nature of the quantum phase diagram of the spin- $1/2$ Heisenberg model on the maple-leaf lattice with three symmetry-inequivalent nearest-neighbor interactions. It has been argued that the parameter regime with antiferromagnetic couplings on hexagons $J_h$ and ferromagnetic couplings on triangles $J_t$ and dimer $J_d$ bonds, is potentially host to a cornucopia of emergent phases with unconventional orders. Our analysis indeed identifies an extended region where any conventional dipolar magnetic order is absent. A hexagonal singlet state is found in the region around $J_{d}=J_{t}=0$ , while a dimerized hexagonal singlet order of a lattice nematic character appears proximate to the phase boundary with the c $120^\circ$ antiferromagnetic order. Interestingly, upon traversing the bulk of the paramagnetic (PM) region, we find a variety of distinct correlation profiles, which are qualitatively different from those of the hexagonal singlet and dimerized hexagonal singlet orders but feature no appreciable spin-nematic response, while the boundary with the ferromagnetic phase shows evidence of spin-nematic order. This PM region is thus likely host to an ensemble of nonmagnetic phases which could putatively include quantum spin liquids. Our phase diagram is built from a complementary application of state-of-the-art implementations of the cluster mean-field and pseudo-fermion functional renormalization group approaches, together with an unconstrained Luttinger-Tisza treatment of the model providing insights from the semi-classical limit.Motivated by the search for unconventional orders in frustrated quantum magnets, we present a multi-method investigation into the nature of the quantum phase diagram of the spin-$1/2$ Heisenberg model on the maple-leaf lattice with three symmetry-inequivalent nearest-neighbor interactions. It has been argued that the parameter regime with antiferromagnetic couplings on hexagons $J_h$ and ferromagnetic couplings on triangles $J_t$ and dimer $J_d$ bonds, is potentially host to a cornucopia of emergent phases with unconventional orders. Our analysis indeed identifies an extended region where any conventional dipolar magnetic order is absent. A hexagonal singlet state is found in the region around $J_{d}=J_{t}=0$, while a dimerized hexagonal singlet order of a lattice nematic character appears proximate to the phase boundary with the c$120^\circ$ antiferromagnetic order. Interestingly, upon traversing the bulk of the paramagnetic (PM) region, we find a variety of distinct correlation profiles, which are qualitatively different from those of the hexagonal singlet and dimerized hexagonal singlet orders but feature no appreciable spin-nematic response, while the boundary with the ferromagnetic phase shows evidence of spin-nematic order. This PM region is thus likely host to an ensemble of nonmagnetic phases which could putatively include quantum spin liquids. Our phase diagram is built from a complementary application of state-of-the-art implementations of the cluster mean-field and pseudo-fermion functional renormalization group approaches, together with an unconstrained Luttinger-Tisza treatment of the model providing insights from the semi-classical limit.

cond-mat.str-elCross-listedarXiv:2511.21598Zeitschrift für Naturforschung ANov 27, 20252 citations

Competing Paramagnetic Phases in the Maple-Leaf Heisenberg Antiferromagnet

Paul L. Ebert, Yasir Iqbal, Alexander Wietek

We establish a remarkably rich ground state phase diagram in the maple-leaf lattice spin- $1/2$ Heisenberg antiferromagnet as a function of the three symmetry-inequivalent nearest-neighbor bonds using exact diagonalization and tower-of-states analysis on clusters up to $N=36$ sites. Besides a hexagonal plaquette state, a star-shaped valence bond solid state is discovered in close vicinity to the (canted) $120^\circ$ magnetic phase, strongly reminiscent of a de-confined critical point or Dirac spin liquid scenario on the triangular lattice antiferromagnets. Moreover, an exact dimer product-state is observed next to a collinear Néel-state, similar to the Shastry-Sutherland model. All identified phases compete in a parameter regime close to the isotropic point, providing a promising region for spin liquids to emerge. By analyzing Gutzwiller-projected wave-functions we identify a sliver of parameter regime where a gapped $\mathbb{Z}_{2}$ spin liquid Ansatz is in astonishing agreement with the exact $N=36$ ground state. This rich competition of paramagnetic phases demonstrates that the maple-leaf antiferromagnet is a promising platform for exotic states of matter and quantum critical phenomena.We establish a remarkably rich ground state phase diagram in the maple-leaf lattice spin-$1/2$ Heisenberg antiferromagnet as a function of the three symmetry-inequivalent nearest-neighbor bonds using exact diagonalization and tower-of-states analysis on clusters up to $N=36$ sites. Besides a hexagonal plaquette state, a star-shaped valence bond solid state is discovered in close vicinity to the (canted) $120^\circ$ magnetic phase, strongly reminiscent of a de-confined critical point or Dirac spin liquid scenario on the triangular lattice antiferromagnets. Moreover, an exact dimer product-state is observed next to a collinear Néel-state, similar to the Shastry-Sutherland model. All identified phases compete in a parameter regime close to the isotropic point, providing a promising region for spin liquids to emerge. By analyzing Gutzwiller-projected wave-functions we identify a sliver of parameter regime where a gapped $\mathbb{Z}_{2}$ spin liquid Ansatz is in astonishing agreement with the exact $N=36$ ground state. This rich competition of paramagnetic phases demonstrates that the maple-leaf antiferromagnet is a promising platform for exotic states of matter and quantum critical phenomena.

arXiv:2601.05308Jan 8, 20260 citations

Triplon analysis of magnetic disorder and order in maple-leaf Heisenberg magnet

Pratyay Ghosh

), is investigated in a parameter regime whereJh>0andJt,Jd<0. This investigation aims to identify regions hosting exotic valence-bond solid states. Two potential magnetically disordered ground states are identified, and their stability is assessed through plaquette-triplon mean-field analyses. The resulting quantum phase diagram reveals that at large|Jt|and|Jd|, the system adopts a magnetically disordered dimerized VBS state, while for small|Jd|, it stabilizes a Néel state. A second-order phase transition from the dimerized phase to a Néel phase is observed, which, being Landau-forbidden, suggests the potential presence of exotic phenomena such as a deconfined quantum critical point or the appearance of a quantum spin liquid. This work provides insights into the phase diagram of the nearest-neighbor spin-1/2 Heisenberg model on the maple-leaf lattice and lays the groundwork for further investigations into its intriguing physics.), is investigated in a parameter regime whereJh>0andJt,Jd<0. This investigation aims to identify regions hosting exotic valence-bond solid states. Two potential magnetically disordered ground states are identified, and their stability is assessed through plaquette-triplon mean-field analyses. The resulting quantum phase diagram reveals that at large|Jt|and|Jd|, the system adopts a magnetically disordered dimerized VBS state, while for small|Jd|, it stabilizes a Néel state. A second-order phase transition from the dimerized phase to a Néel phase is observed, which, being Landau-forbidden, suggests the potential presence of exotic phenomena such as a deconfined quantum critical point or the appearance of a quantum spin liquid. This work provides insights into the phase diagram of the nearest-neighbor spin-1/2 Heisenberg model on the maple-leaf lattice and lays the groundwork for further investigations into its intriguing physics.

Journal of Physics Condensed MatterJul 31, 202414 citations

Tensor-network study of the ground state of maple-leaf Heisenberg antiferromagnet

Samuel Nyckees, Pratyay Ghosh, Frédéric Mila

We study the quantum phase diagram of the spin- $1/2$ nearest-neighbor Heisenberg model on the maple-leaf lattice using infinite projected entangled pair states (iPEPS) combined with a corner transfer matrix renormalization group scheme adapted to $C_3$ -symmetric lattices. Focusing on the fully antiferromagnetic $J$ - $J_d$ model with $J_h = J_t := J$ , we map out the ground-state phase diagram as a function of the dimer coupling $J_d$ . Our results show that the system hosts only two phases: a magnetically ordered canted- $120^\circ$ phase and an exact dimer singlet product phase. We identify a first-order transition between these two phases at $J_d/J \approx 1.45$ . Within the magnetically ordered phase, we observe small but finite magnetic moments. We also resolve the quantum renormalization of the canting angle, which deviates from the classical prediction over almost the entire magnetically ordered phase.We study the quantum phase diagram of the spin-$1/2$ nearest-neighbor Heisenberg model on the maple-leaf lattice using infinite projected entangled pair states (iPEPS) combined with a corner transfer matrix renormalization group scheme adapted to $C_3$-symmetric lattices. Focusing on the fully antiferromagnetic $J$-$J_d$ model with $J_h = J_t := J$, we map out the ground-state phase diagram as a function of the dimer coupling $J_d$. Our results show that the system hosts only two phases: a magnetically ordered canted-$120^\circ$ phase and an exact dimer singlet product phase. We identify a first-order transition between these two phases at $J_d/J \approx 1.45$. Within the magnetically ordered phase, we observe small but finite magnetic moments. We also resolve the quantum renormalization of the canting angle, which deviates from the classical prediction over almost the entire magnetically ordered phase.

arXiv:2512.20466Dec 23, 20250 citations

Phase diagram of the J − J d Heisenberg model on the maple leaf lattice: Neural networks and density matrix renormalization group

Jonas Beck, Jonathan Bodky, Johannes Motruk +3 more

We microscopically analyze the nearest-neighbor Heisenberg model on the maple leaf lattice through neural quantum state (NQS) and infinite density matrix renormalization group (iDMRG) methods. Embarking to parameter regimes beyond the exact dimer singlet ground state with a dimer bond spin exchange coupling ${J}_{d}$ varied against the exchange strength $J$ of all other bonds, the iDMRG (NQS) method finds a dimer state paramagnetic phase for ${J}_{d}/J>1.464$ ( ${J}_{d}/J>1.39$ ) and a canted ${120}^{\ensuremath{\circ}}$ magnetic order for ${J}_{d}/J<1.419$ ( ${J}_{d}/J<1.23$ ). Assessing training convergence inaccuracies of the NQS method and the influence of finite cylindric circumference in the iDMRG method, we discuss the possible existence of an intermediate phase between the magnet and the dimer paramagnet.We microscopically analyze the nearest-neighbor Heisenberg model on the maple leaf lattice through neural quantum state (NQS) and infinite density matrix renormalization group (iDMRG) methods. Embarking to parameter regimes beyond the exact dimer singlet ground state with a dimer bond spin exchange coupling ${J}_{d}$ varied against the exchange strength $J$ of all other bonds, the iDMRG (NQS) method finds a dimer state paramagnetic phase for ${J}_{d}/J>1.464$ (${J}_{d}/J>1.39$) and a canted ${120}^{\ensuremath{\circ}}$ magnetic order for ${J}_{d}/J<1.419$ (${J}_{d}/J<1.23$). Assessing training convergence inaccuracies of the NQS method and the influence of finite cylindric circumference in the iDMRG method, we discuss the possible existence of an intermediate phase between the magnet and the dimer paramagnet.

arXiv:2401.04995Physical review. B./Physical review. BMay 10, 202421 citations

1/2

Heisenberg antiferromagnet on the maple-leaf lattice, which is known to relieve frustration by the formation of canted

{120}^{\ensuremath{\circ}}

We investigate the possibility of exotic phenomena, viz. quantum spin liquid (QSL) or deconfined quantum critical point (DQCP), in the spin-

\frac{1}{2}

Heisenberg model on the maple-leaf lattice, a geometrically frustrated system formed by hexagons (coupling

J_h

), triangles (coupling

J_t

), and dimers (coupling

J_d

). We identify one promising region, given by

J_h > 0

and

J_t, J_d < 0

, for hosting enticing physics. In this region, the quantum phase diagram of the system exhibits an interplay between Néel order and a gapped dimerized singlet phase. This arrangement holds the possibility of harboring a QSL and a DQCP. Using bond-operator mean-field theory and density matrix renormalization group calculations, we delve into this uncharted territory, revealing tantalizing evidence of the existence of a QSL phase and highlighting its potential as a platform for DQCP.

Motivated by the search for unconventional orders in frustrated quantum magnets, we present a multi-method investigation into the nature of the quantum phase diagram of the spin-

1/2

Heisenberg model on the maple-leaf lattice with three symmetry-inequivalent nearest-neighbor interactions. It has been argued that the parameter regime with antiferromagnetic couplings on hexagons

J_h

and ferromagnetic couplings on triangles

J_t

and dimer

J_d

bonds, is potentially host to a cornucopia of emergent phases with unconventional orders. Our analysis indeed identifies an extended region where any conventional dipolar magnetic order is absent. A hexagonal singlet state is found in the region around

J_{d}=J_{t}=0

, while a dimerized hexagonal singlet order of a lattice nematic character appears proximate to the phase boundary with the c

120^\circ

antiferromagnetic order. Interestingly, upon traversing the bulk of the paramagnetic (PM) region, we find a variety of distinct correlation profiles, which are qualitatively different from those of the hexagonal singlet and dimerized hexagonal singlet orders but feature no appreciable spin-nematic response, while the boundary with the ferromagnetic phase shows evidence of spin-nematic order. This PM region is thus likely host to an ensemble of nonmagnetic phases which could putatively include quantum spin liquids. Our phase diagram is built from a complementary application of state-of-the-art implementations of the cluster mean-field and pseudo-fermion functional renormalization group approaches, together with an unconstrained Luttinger-Tisza treatment of the model providing insights from the semi-classical limit.

We establish a remarkably rich ground state phase diagram in the maple-leaf lattice spin-

1/2

Heisenberg antiferromagnet as a function of the three symmetry-inequivalent nearest-neighbor bonds using exact diagonalization and tower-of-states analysis on clusters up to

N=36

sites. Besides a hexagonal plaquette state, a star-shaped valence bond solid state is discovered in close vicinity to the (canted)

120^\circ

magnetic phase, strongly reminiscent of a de-confined critical point or Dirac spin liquid scenario on the triangular lattice antiferromagnets. Moreover, an exact dimer product-state is observed next to a collinear Néel-state, similar to the Shastry-Sutherland model. All identified phases compete in a parameter regime close to the isotropic point, providing a promising region for spin liquids to emerge. By analyzing Gutzwiller-projected wave-functions we identify a sliver of parameter regime where a gapped

\mathbb{Z}_{2}

spin liquid Ansatz is in astonishing agreement with the exact

N=36

ground state. This rich competition of paramagnetic phases demonstrates that the maple-leaf antiferromagnet is a promising platform for exotic states of matter and quantum critical phenomena.

We study the quantum phase diagram of the spin-

1/2

nearest-neighbor Heisenberg model on the maple-leaf lattice using infinite projected entangled pair states (iPEPS) combined with a corner transfer matrix renormalization group scheme adapted to

C_3

-symmetric lattices. Focusing on the fully antiferromagnetic

J

J_d

model with

J_h = J_t := J

, we map out the ground-state phase diagram as a function of the dimer coupling

J_d

. Our results show that the system hosts only two phases: a magnetically ordered canted-

120^\circ

phase and an exact dimer singlet product phase. We identify a first-order transition between these two phases at

J_d/J \approx 1.45

. Within the magnetically ordered phase, we observe small but finite magnetic moments. We also resolve the quantum renormalization of the canting angle, which deviates from the classical prediction over almost the entire magnetically ordered phase.

{J}_{d}

varied against the exchange strength

J

of all other bonds, the iDMRG (NQS) method finds a dimer state paramagnetic phase for

{J}_{d}/J>1.464

(

{J}_{d}/J>1.39

) and a canted ${120}^{\ensuremath{\circ}}$ magnetic order for

{J}_{d}/J<1.419

(

{J}_{d}/J<1.23

). Assessing training convergence inaccuracies of the NQS method and the influence of finite cylindric circumference in the iDMRG method, we discuss the possible existence of an intermediate phase between the magnet and the dimer paramagnet.