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:2610.03186

Topological phase transition in a symmetric blockade structure

Johannes Mögerle, Simon Fell, Tobias F. Maier, Ali Otaifi, Lode Pollet, Nicolai Lang, Hans Peter Büchler

quant-phcond-mat.quant-gascond-mat.str-elSubmitted Oct 2, 2026• Announced Oct 5, 2026• 0 citations
arXivHTMLPDF

Abstract

We present a numerical study of a blockade Hamiltonian with a local $\mathbb{Z}_2$ symmetry. For such models, the existence of a topologically ordered ground state has been proven rigorously for weak Rabi driving [T. F. Maier et al., PRX Quantum 6, 030340 (2025)]. However, the phase diagram beyond weak driving is still an open question. We perform large-scale infinite-size density matrix renormalization group (iDMRG) simulations on a cylinder and map out the full phase diagram of the model. We find a single continuous phase transition between the topologically ordered phase and a trivial paramagnetic phase, and confirm numerically the stability of the topologically ordered phase up to Rabi drives comparable to the characteristic energy scale of the system. Furthermore, we compute the excitation gaps and show that the charge gap remains open across the phase transition and charges become confined in the trivial phase. On the other hand, the gap in the symmetric sector closes at the transition, consistent with the condensation of flux excitations.

Comments
14 pages, 6 figures

Related papers

Excitation gap of a blockade structure with $\mathbb{Z}_2$ topological order

Simon Fell, Tobias F. Maier, Hans Peter Büchler +1 more

Mathematically rigorous statements on the spectral gap of quantum many-body systems in the thermodynamic limit are notoriously difficult to prove -- yet they are of fundamental importance for classifying quantum phases of matter. Here we prove the existence of a finite excitation gap for a particular Hamiltonian which was proposed in [T. F. Maier et al., PRX Quantum 6, 030340 (2025)] and is motivated by the Rydberg platform. The Hamiltonian exhibits only two-body blockade interactions between two-level systems and has a topologically ordered ground state in the toric code phase. We show that our result also applies to a broader class of blockade Hamiltonians which realize non-Abelian quantum double phases and were proposed in [H. P. Büchler et al., Phys. Rev. B 114, 065113 (2026)]. The proof builds on known gap stability results and exploits the local symmetry of the studied models.

quant-pharXiv:2609.39475•Oct 1, 2026•0 citations

Symmetry fractionalization in the topological phase of the spin- 1 2 J 1 − J 2 triangular Heisenberg model

S. N. Saadatmand, Ian P. McCulloch

Using density-matrix renormalization-group calculations for infinite cylinders, we elucidate the properties of the spin-liquid phase of the spin-$\frac{1}{2}\phantom{\rule{4pt}{0ex}}{J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the triangular lattice. We find four distinct ground states characteristic of a nonchiral, ${Z}_{2}$ topologically ordered state with vison and spinon excitations. We shed light on the interplay of topological ordering and global symmetries in the model by detecting fractionalization of time-reversal and space-group dihedral symmetries in the anyonic sectors, which leads to the coexistence of symmetry protected and intrinsic topological order. The anyonic sectors, and information on the particle statistics, can be characterized by degeneracy patterns and symmetries of the entanglement spectrum. We demonstrate the ground states on finite-width cylinders are short-range correlated and gapped; however, some features in the entanglement spectrum suggest that the system develops gapless spinonlike edge excitations in the large-width limit.

arXiv:1606.00334•Physical review. B./Physical review. B•Sep 13, 2016•71 citations

Topological phase transition and the effect of Hubbard interactions on the one-dimensional topological Kondo insulator

Jason C. Pillay, Ian P. McCulloch

The effect of a local Kondo coupling and Hubbard interaction on the topological phase of the one-dimensional topological Kondo insulator (TKI) is numerically investigated using the infinite matrix-product state density-matrix renormalization group algorithm. The ground state of the TKI is a symmetry-protected topological (SPT) phase protected by inversion symmetry. It is found that on its own, the Hubbard interaction that tends to force fermions into a one-charge per site order is insufficient to destroy the SPT phase. However, when the local Kondo Hamiltonian term that favors a topologically trivial ground state with a one-charge per site order is introduced, the Hubbard interaction assists in the destruction of the SPT phase. This topological phase transition occurs in the charge sector where the correlation length of the charge excitation diverges while the correlation length of the spin excitation remains finite. The critical exponents, central charge, and the phase diagram separating the SPT phase from the topologically trivial phase are presented.

arXiv:1801.01279•Physical review. B./Physical review. B•May 25, 2018•6 citations

From trivial to topological paramagnets: The case of Z2 and Z23 symmetries in two dimensions

Maxime Dupont, Snir Gazit, Thomas Scaffidi

Using quantum Monte Carlo simulations, we map out the phase diagram of Hamiltonians interpolating between trivial and nontrivial bosonic symmetry-protected topological phases, protected by ${\mathbb{Z}}_{2}$ and ${\mathbb{Z}}_{2}^{3}$ symmetries, in two dimensions. In all cases, we find that the trivial and the topological phases are separated by an intermediate phase in which the protecting symmetry is spontaneously broken. Depending on the model, we identify a variety of magnetic orders on the triangular lattice, including ferromagnetism, $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ order, and stripe orders (both commensurate and incommensurate). Critical properties are determined through a finite-size scaling analysis. Possible scenarios regarding the nature of the phase transitions are discussed.

arXiv:2008.11206•Physical review. B./Physical review. B•Apr 30, 2021•28 citations

Phases and phase transitions in a dimerized spin-$\mathbf{\frac{1}{2}}$ XXZ chain

Harsh Nigam, Ashirbad Padhan, Diptiman Sen +2 more

We revisit the phase diagram of the dimerized XXZ spin-$\frac{1}{2}$ chain with nearest-neighbor couplings which was studied numerically in Phys. Rev. B 106, L201106 (2022). The model has isotropic $XY$ couplings which have a uniform value and $ZZ$ couplings which have a dimerized form, with strengths $J_a$ and $J_b$ on alternate bonds. We find a rich phase diagram in the region of positive $J_a, ~J_b$. We provide a detailed understanding of the different phases and associated quantum phase transitions using a combination of mean-field theory, low-energy effective Hamiltonians, renormalization group calculations employing the technique of bosonization, and numerical calculations using the density-matrix renormalization group (DMRG) method. The phase diagram consists of two Ising paramagnetic phases called IPM$_0$ and IPM$_π$, and a phase with Ising Neel order called IN; all these phases are gapped. The phases IPM$_0$ and IPM$_π$ are separated by a gapless phase transition line given by $0 \le J_a = J_b \le 1$ which is described by a conformal field theory with central charge $c=1$. There are two gapless phase transition lines separating IPM$_0$ from IN and IPM$_π$ from IN; these are described by conformal field theories with $c=\frac{1}{2}$ corresponding to quantum Ising transitions. The $c=1$ line bifurcates into the two $c=\frac{1}{2}$ lines at the point $J_a = J_b = 1$; the shape of the bifurcation is found analytically using RG calculations. A symmetry analysis shows that IPM$_0$ is a topologically trivial phase while IPM$_π$ is a time-reversal symmetry-protected topological phase (SPT) with spin-$\frac{1}{2}$ states at the two ends of an open system. The numerical results obtained by the DMRG method are in good agreement with the analytical results. Finally we propose experimental platforms for testing our results.

arXiv:2408.14474•Aug 26, 2024•0 citations

Gapped Topological Spin-Orbital Liquid on the Honeycomb Lattice

Masahiko G. Yamada

We perform large-scale density matrix renormalization group simulations of the SU(4) Heisenberg model on the honeycomb lattice to address the long-standing question of its ground state in an unbiased and quantitatively controlled manner. We find reliable numerical evidence that the ground state is a gapped spin-orbital liquid, presumably with a Z_{4} topological order, characterized by a finite topological entanglement entropy close to ln(4), the absence of both SU(4) and lattice symmetry breaking, and a variationally optimized ground-state energy well below the previously proposed π-flux variational state. By exploiting full SU(4) symmetry and keeping up to 12 800 SU(4) multiplets, corresponding to more than 1×10^{6} U(1) states, we achieve unprecedented accuracy for two-dimensional SU(4) quantum magnets. Finite-size scaling of energies and entanglement entropies supports a robust gapped phase in the two-dimensional limit, while a gapless critical state on narrow cylinders is identified as a proximate remnant of a Dirac spin-orbital liquid. Our results find the SU(4) honeycomb Heisenberg model a realization of a gapped topological spin-orbital liquid and provide convincing numerical evidence for topological order in a highly symmetric two-dimensional quantum magnet.

arXiv:2601.06549•Physical Review Letters•Sep 10, 2026•0 citations
We present a numerical study of a blockade Hamiltonian with a local Z2\mathbb{Z}_2Z2​ symmetry. For such models, the existence of a topologically ordered ground state has been proven rigorously for weak Rabi driving [T. F. Maier et al., PRX Quantum 6, 030340 (2025)]. However, the phase diagram beyond weak driving is still an open question. We perform large-scale infinite-size density matrix renormalization group (iDMRG) simulations on a cylinder and map out the full phase diagram of the model. We find a single continuous phase transition between the topologically ordered phase and a trivial paramagnetic phase, and confirm numerically the stability of the topologically ordered phase up to Rabi drives comparable to the characteristic energy scale of the system. Furthermore, we compute the excitation gaps and show that the charge gap remains open across the phase transition and charges become confined in the trivial phase. On the other hand, the gap in the symmetric sector closes at the transition, consistent with the condensation of flux excitations.
Excitation gap of a blockade structure with Z2\mathbb{Z}_2Z2​ topological order
Mathematically rigorous statements on the spectral gap of quantum many-body systems in the thermodynamic limit are notoriously difficult to prove -- yet they are of fundamental importance for classifying quantum phases of matter. Here we prove the existence of a finite excitation gap for a particular Hamiltonian which was proposed in [T. F. Maier et al., PRX Quantum 6, 030340 (2025)] and is motivated by the Rydberg platform. The Hamiltonian exhibits only two-body blockade interactions between two-level systems and has a topologically ordered ground state in the toric code phase. We show that our result also applies to a broader class of blockade Hamiltonians which realize non-Abelian quantum double phases and were proposed in [H. P. Büchler et al., Phys. Rev. B 114, 065113 (2026)]. The proof builds on known gap stability results and exploits the local symmetry of the studied models.
Using density-matrix renormalization-group calculations for infinite cylinders, we elucidate the properties of the spin-liquid phase of the spin-$\frac{1}{2}\phantom{\rule{4pt}{0ex}}{J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the triangular lattice. We find four distinct ground states characteristic of a nonchiral, Z2{Z}_{2}Z2​ topologically ordered state with vison and spinon excitations. We shed light on the interplay of topological ordering and global symmetries in the model by detecting fractionalization of time-reversal and space-group dihedral symmetries in the anyonic sectors, which leads to the coexistence of symmetry protected and intrinsic topological order. The anyonic sectors, and information on the particle statistics, can be characterized by degeneracy patterns and symmetries of the entanglement spectrum. We demonstrate the ground states on finite-width cylinders are short-range correlated and gapped; however, some features in the entanglement spectrum suggest that the system develops gapless spinonlike edge excitations in the large-width limit.
The effect of a local Kondo coupling and Hubbard interaction on the topological phase of the one-dimensional topological Kondo insulator (TKI) is numerically investigated using the infinite matrix-product state density-matrix renormalization group algorithm. The ground state of the TKI is a symmetry-protected topological (SPT) phase protected by inversion symmetry. It is found that on its own, the Hubbard interaction that tends to force fermions into a one-charge per site order is insufficient to destroy the SPT phase. However, when the local Kondo Hamiltonian term that favors a topologically trivial ground state with a one-charge per site order is introduced, the Hubbard interaction assists in the destruction of the SPT phase. This topological phase transition occurs in the charge sector where the correlation length of the charge excitation diverges while the correlation length of the spin excitation remains finite. The critical exponents, central charge, and the phase diagram separating the SPT phase from the topologically trivial phase are presented.
Using quantum Monte Carlo simulations, we map out the phase diagram of Hamiltonians interpolating between trivial and nontrivial bosonic symmetry-protected topological phases, protected by Z2{\mathbb{Z}}_{2}Z2​ and Z23{\mathbb{Z}}_{2}^{3}Z23​ symmetries, in two dimensions. In all cases, we find that the trivial and the topological phases are separated by an intermediate phase in which the protecting symmetry is spontaneously broken. Depending on the model, we identify a variety of magnetic orders on the triangular lattice, including ferromagnetism, $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ order, and stripe orders (both commensurate and incommensurate). Critical properties are determined through a finite-size scaling analysis. Possible scenarios regarding the nature of the phase transitions are discussed.
Phases and phase transitions in a dimerized spin-12\mathbf{\frac{1}{2}}21​ XXZ chain
We revisit the phase diagram of the dimerized XXZ spin-12\frac{1}{2}21​ chain with nearest-neighbor couplings which was studied numerically in Phys. Rev. B 106, L201106 (2022). The model has isotropic XYXYXY couplings which have a uniform value and ZZZZZZ couplings which have a dimerized form, with strengths JaJ_aJa​ and JbJ_bJb​ on alternate bonds. We find a rich phase diagram in the region of positive Ja, JbJ_a, ~J_bJa​, Jb​. We provide a detailed understanding of the different phases and associated quantum phase transitions using a combination of mean-field theory, low-energy effective Hamiltonians, renormalization group calculations employing the technique of bosonization, and numerical calculations using the density-matrix renormalization group (DMRG) method. The phase diagram consists of two Ising paramagnetic phases called IPM0_00​ and IPMπ_ππ​, and a phase with Ising Neel order called IN; all these phases are gapped. The phases IPM0_00​ and IPMπ_ππ​ are separated by a gapless phase transition line given by 0≤Ja=Jb≤10 \le J_a = J_b \le 10≤Ja​=Jb​≤1 which is described by a conformal field theory with central charge c=1c=1c=1. There are two gapless phase transition lines separating IPM0_00​ from IN and IPMπ_ππ​ from IN; these are described by conformal field theories with c=12c=\frac{1}{2}c=21​ corresponding to quantum Ising transitions. The c=1c=1c=1 line bifurcates into the two c=12c=\frac{1}{2}c=21​ lines at the point Ja=Jb=1J_a = J_b = 1Ja​=Jb​=1; the shape of the bifurcation is found analytically using RG calculations. A symmetry analysis shows that IPM0_00​ is a topologically trivial phase while IPMπ_ππ​ is a time-reversal symmetry-protected topological phase (SPT) with spin-12\frac{1}{2}21​ states at the two ends of an open system. The numerical results obtained by the DMRG method are in good agreement with the analytical results. Finally we propose experimental platforms for testing our results.
We perform large-scale density matrix renormalization group simulations of the SU(4) Heisenberg model on the honeycomb lattice to address the long-standing question of its ground state in an unbiased and quantitatively controlled manner. We find reliable numerical evidence that the ground state is a gapped spin-orbital liquid, presumably with a Z_{4} topological order, characterized by a finite topological entanglement entropy close to ln(4), the absence of both SU(4) and lattice symmetry breaking, and a variationally optimized ground-state energy well below the previously proposed π-flux variational state. By exploiting full SU(4) symmetry and keeping up to 12 800 SU(4) multiplets, corresponding to more than 1×10^{6} U(1) states, we achieve unprecedented accuracy for two-dimensional SU(4) quantum magnets. Finite-size scaling of energies and entanglement entropies supports a robust gapped phase in the two-dimensional limit, while a gapless critical state on narrow cylinders is identified as a proximate remnant of a Dirac spin-orbital liquid. Our results find the SU(4) honeycomb Heisenberg model a realization of a gapped topological spin-orbital liquid and provide convincing numerical evidence for topological order in a highly symmetric two-dimensional quantum magnet.