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:1909.13457 · Physical review. B./Physical review. B

Topological order versus many-body localization in periodically modulated spin chains

Takahiro Orito, Yoshihito Kuno, Ikuo Ichinose

Published Dec 3, 2019• 9 citations
arXivHTMLPDF

Abstract

In this paper, we study periodically modulated $s=1/2$ spin chain in a linear gradient potential (LP) that is generated by an external magnetic field. In the absence of the LP, the system has topological states that exhibit a magnetization plateau for a uniform external magnetic field. These topological states have a finite integer Chern number and their stability is clarified by an equivalent spinless fermion system derived by a Jordan-Wigner transformation. We show that the LP, which is nothing but a constant electric field in the spinless fermion system, destabilizes the topological states, because it induces localization called Wannier-Stark (WS) localization. We clarify the phase diagram in the presence of the LP and on-site diagonal disorder. To this end, we carefully study edge excitations under the open boundary condition, which are a hallmark of the topological order. We find a very interesting phenomenon indicating existence of a quasiedge modes that take the place of the genuine edge modes in certain parameter regions. This is a precursor of the WS localization realized in topological states. Finally, we investigate many-body localization induced by a sufficiently strong LP or disorder. To this end, we study the energy-level statistics for whole energy levels, and we find unexpected extended-state regimes located in intermediate potential-gradient and weak on-site disorder regimes. We verify this phenomenon by calculating variance of the entanglement entropy. The present system is closely related to quantum Hall state in two dimensions, and therefore our findings can be observed not only in experiments on ultracold atomic gases but also quantum Hall physics.

DOI
10.1103/physrevb.100.214202

Related papers

On Stark Many-body localization perturbed by harmonic potential

Ruixiao Yao, Titas Chanda, Jakub Zakrzewski

We discuss properties of interacting spinless fermions in a tilted optical lattice as modeled by Heisenberg spin chain in magnetic (or electric) field changing linearly across the chain. The system shows genuine features of strong localization for a sufficiently large tilt with distinct features different from disorder induced localization. In particular, Stark many-body localization is characterized in time dynamics by a linear increase of the entanglement entropy followed by a saturation at a constant, time independent value -- both the number (classical) and the configuration (quantum) entropies saturate to a constant value. Similarly, the correlation with the initial state (the so called imbalance) stabilizes at a constant value (modulo large fluctuations coming from short time Bloch-type oscillations). The presence of an additional harmonic potential profoundly affects the dynamics of the model -- its behavior resembles standard MBL characteristics -- the logarithmic growth of the entanglement entropy in particular. In that case, we find strong revival phenomena associated with the manifold of equally spaced states, degenerate in the absence of the harmonic potential.

•Mar 22, 2021•0 citations

Crossover from Wannier-Stark localization to charge density waves for interacting spinless fermions in one dimension

N. Aucar Boidi, Amnon Aharony A, Ora Entin-wohlman A +2 more

We study spinless fermions on a finite chain with nearest-neighbor repulsion and in the presence of a Wannier-Stark (WS) linearly varying electric field potential. In the absence of the interaction, the eigenstates are localized for system's sizes larger than the localization length. We present several analytical expressions for the localization length, which in all cases is proportional to the inverse of the electric field. Using the density matrix renormalization group numerical technique, we observe that the ground state exhibits a decrease of the occupation on the chain sites from the 'bulk', with occupation 1, to the vacuum, with occupation 0. The width of this intermediate 'edge' region is also inversely proportional to the electric field, increasing linearly with the strength of the nearest-neighbor repulsion. For strong interactions, the occupations in the intermediate region exhibit a charge density wave. We also present the local density of states for sites in the intermediate 'domain wall' region. For the non-interacting case, the spectrum shows an increasing energy-localized structure as the field is increased, which is a consequence of the uniform energy distribution of the localized states (WS ladder). This structure survives for small interactions, and it smears out in the strongly interacting limit. Experimental variations of the slope of the potential (the electric field) on cold atom chains may test these predictions.

arXiv:2502.04866•Journal of Physics Condensed Matter•Sep 12, 2025•0 citations

Topological nature of magnetization plateaus in periodically modulated quantum spin chains

Haiping Hu, Chen Cheng, Zhihao Xu +2 more

We unveil nontrivial topological properties of zero-temperature magnetization plateau states in periodically modulated quantum spin chains under a uniform magnetic field. As positions of plateaus are uniquely determined by the modulation period of exchange couplings, we find that the topologically nontrivial plateau state can be characterized by a nonzero integer Chern number and has nontrivial edge excitations. Our study clarifies the topological origin of the well-known phenomena of quantized magnetization plateaus in one-dimensional quantum spin systems and relates the plateau state to the correlated topological insulator.

arXiv:1310.4551•Physical Review B•Jul 31, 2014•30 citations

Topological spin excitations in Harper-Heisenberg spin chains

José Luis Lado, Oded Zilberberg

Many-body spin systems represent a paradigmatic platform for the realization of emergent states of matter in a strongly interacting regime. Spin models are commonly studied in one-dimensional periodic chains, whose lattice constant is on the order of the interatomic distance. However, in cold atomic setups or functionalized twisted van der Waals heterostructures, long-range modulations of the spin physics can be engineered. Here we show that such superlattice modulations in a many-body spin Hamiltonian can give rise to observable topological boundary modes in the excitation spectrum of the spin chain. In the case of an XY spin-1/2 chain, these boundary modes stem from a mathematical correspondence with the chiral edge modes of a two-dimensional quantum Hall state. Our results show that the addition of many-body interactions does not close some of the topological gaps in the excitation spectrum, and the topological boundary modes visibly persist in the isotropic Heisenberg limit. These observations carry through when the spin moment is increased and a large-spin limit of the phenomenon is established. Our results show that such spin superlattices provide a promising route to observe many-body topological boundary effects in cold atomic setups and functionalized twisted van der Waals materials.

•Dec 1, 2019•34 citations

Stark Many-Body Localization

Maximilian Schulz, C. Hooley, Roderich Moessner +1 more

We consider spinless fermions on a finite one-dimensional lattice, interacting via nearest-neighbor repulsion and subject to a strong electric field. In the noninteracting case, due to Wannier-Stark localization, the single-particle wave functions are exponentially localized even though the model has no quenched disorder. We show that this system remains localized in the presence of interactions and exhibits physics analogous to models of conventional many-body localization (MBL). In particular, the entanglement entropy grows logarithmically with time after a quench, albeit with a slightly different functional form from the MBL case, and the level statistics of the many-body energy spectrum are Poissonian. We moreover predict that a quench experiment starting from a charge-density wave state would show results similar to those of Schreiber et al. [Science 349, 842 (2015)SCIEAS0036-807510.1126/science.aaa7432].

arXiv:1808.01250•Physical Review Letters•Jan 30, 2019•253 citations

Enhanced superconductivity and various edge modes in modulated t−J chains

Yong-Feng Yang, Jing Chen, Chen Cheng +1 more

We numerically investigate the ground state of the extended $t\text{\ensuremath{-}}J$ Hamiltonian with periodic local modulations in one dimension by using the density-matrix renormalization group method. Examining charge and spin excitation gaps, as well as the pair binding energy, with extrapolated results to the thermodynamic limit, we obtain a rich ground-state phase diagram consisting of the metallic state, the superconducting state, the phase separation, and insulating states at commensurate fillings. Compared to the homogeneous one-dimensional (1D) $t\text{\ensuremath{-}}J$ model, the superconductivity is greatly enhanced and stabilized by the flat-band structure. This superconducting state in periodically modulated chains shares similar properties with ladder systems: significant negative pair binding energy occurs, and the singlet-pairing correlation function dominates with the algebraic decay while the single-particle Green's function and spin correlation function decay exponentially. On the other hand, the superlattice structure leads to nontrivial topological nature in insulating states, characterized by different integer Chern numbers at different fillings. Due to the interplay among the topology, the interaction, and the 1D confinement, gapless edge modes show strong spin-charge separation and in different regions can relate to different collective modes, which are the charge of a single fermion, the magnon, and the singlet pair. We also find two interaction-driven topological transitions: (i) at particle filling $\ensuremath{\rho}=\frac{1}{2}$, the low-energy edge excitations change from the magnon to singlet pair, accompanied with pair formation in bulk; and (ii) at $\ensuremath{\rho}=\frac{3}{4}$, while the gapless edge mode is always the charge of a single fermion, there is a gap-closing point and a $\ensuremath{\pi}$-phase shift in the quasiparticle spectrum.

arXiv:2111.13718•Physical review. B./Physical review. B•Apr 14, 2022•3 citations
In this paper, we study periodically modulated s=1/2s=1/2s=1/2 spin chain in a linear gradient potential (LP) that is generated by an external magnetic field. In the absence of the LP, the system has topological states that exhibit a magnetization plateau for a uniform external magnetic field. These topological states have a finite integer Chern number and their stability is clarified by an equivalent spinless fermion system derived by a Jordan-Wigner transformation. We show that the LP, which is nothing but a constant electric field in the spinless fermion system, destabilizes the topological states, because it induces localization called Wannier-Stark (WS) localization. We clarify the phase diagram in the presence of the LP and on-site diagonal disorder. To this end, we carefully study edge excitations under the open boundary condition, which are a hallmark of the topological order. We find a very interesting phenomenon indicating existence of a quasiedge modes that take the place of the genuine edge modes in certain parameter regions. This is a precursor of the WS localization realized in topological states. Finally, we investigate many-body localization induced by a sufficiently strong LP or disorder. To this end, we study the energy-level statistics for whole energy levels, and we find unexpected extended-state regimes located in intermediate potential-gradient and weak on-site disorder regimes. We verify this phenomenon by calculating variance of the entanglement entropy. The present system is closely related to quantum Hall state in two dimensions, and therefore our findings can be observed not only in experiments on ultracold atomic gases but also quantum Hall physics.
We discuss properties of interacting spinless fermions in a tilted optical lattice as modeled by Heisenberg spin chain in magnetic (or electric) field changing linearly across the chain. The system shows genuine features of strong localization for a sufficiently large tilt with distinct features different from disorder induced localization. In particular, Stark many-body localization is characterized in time dynamics by a linear increase of the entanglement entropy followed by a saturation at a constant, time independent value -- both the number (classical) and the configuration (quantum) entropies saturate to a constant value. Similarly, the correlation with the initial state (the so called imbalance) stabilizes at a constant value (modulo large fluctuations coming from short time Bloch-type oscillations). The presence of an additional harmonic potential profoundly affects the dynamics of the model -- its behavior resembles standard MBL characteristics -- the logarithmic growth of the entanglement entropy in particular. In that case, we find strong revival phenomena associated with the manifold of equally spaced states, degenerate in the absence of the harmonic potential.
We study spinless fermions on a finite chain with nearest-neighbor repulsion and in the presence of a Wannier-Stark (WS) linearly varying electric field potential. In the absence of the interaction, the eigenstates are localized for system's sizes larger than the localization length. We present several analytical expressions for the localization length, which in all cases is proportional to the inverse of the electric field. Using the density matrix renormalization group numerical technique, we observe that the ground state exhibits a decrease of the occupation on the chain sites from the 'bulk', with occupation 1, to the vacuum, with occupation 0. The width of this intermediate 'edge' region is also inversely proportional to the electric field, increasing linearly with the strength of the nearest-neighbor repulsion. For strong interactions, the occupations in the intermediate region exhibit a charge density wave. We also present the local density of states for sites in the intermediate 'domain wall' region. For the non-interacting case, the spectrum shows an increasing energy-localized structure as the field is increased, which is a consequence of the uniform energy distribution of the localized states (WS ladder). This structure survives for small interactions, and it smears out in the strongly interacting limit. Experimental variations of the slope of the potential (the electric field) on cold atom chains may test these predictions.
We unveil nontrivial topological properties of zero-temperature magnetization plateau states in periodically modulated quantum spin chains under a uniform magnetic field. As positions of plateaus are uniquely determined by the modulation period of exchange couplings, we find that the topologically nontrivial plateau state can be characterized by a nonzero integer Chern number and has nontrivial edge excitations. Our study clarifies the topological origin of the well-known phenomena of quantized magnetization plateaus in one-dimensional quantum spin systems and relates the plateau state to the correlated topological insulator.
Many-body spin systems represent a paradigmatic platform for the realization of emergent states of matter in a strongly interacting regime. Spin models are commonly studied in one-dimensional periodic chains, whose lattice constant is on the order of the interatomic distance. However, in cold atomic setups or functionalized twisted van der Waals heterostructures, long-range modulations of the spin physics can be engineered. Here we show that such superlattice modulations in a many-body spin Hamiltonian can give rise to observable topological boundary modes in the excitation spectrum of the spin chain. In the case of an XY spin-1/2 chain, these boundary modes stem from a mathematical correspondence with the chiral edge modes of a two-dimensional quantum Hall state. Our results show that the addition of many-body interactions does not close some of the topological gaps in the excitation spectrum, and the topological boundary modes visibly persist in the isotropic Heisenberg limit. These observations carry through when the spin moment is increased and a large-spin limit of the phenomenon is established. Our results show that such spin superlattices provide a promising route to observe many-body topological boundary effects in cold atomic setups and functionalized twisted van der Waals materials.
We consider spinless fermions on a finite one-dimensional lattice, interacting via nearest-neighbor repulsion and subject to a strong electric field. In the noninteracting case, due to Wannier-Stark localization, the single-particle wave functions are exponentially localized even though the model has no quenched disorder. We show that this system remains localized in the presence of interactions and exhibits physics analogous to models of conventional many-body localization (MBL). In particular, the entanglement entropy grows logarithmically with time after a quench, albeit with a slightly different functional form from the MBL case, and the level statistics of the many-body energy spectrum are Poissonian. We moreover predict that a quench experiment starting from a charge-density wave state would show results similar to those of Schreiber et al. [Science 349, 842 (2015)SCIEAS0036-807510.1126/science.aaa7432].
We numerically investigate the ground state of the extended $t\text{\ensuremath{-}}J$ Hamiltonian with periodic local modulations in one dimension by using the density-matrix renormalization group method. Examining charge and spin excitation gaps, as well as the pair binding energy, with extrapolated results to the thermodynamic limit, we obtain a rich ground-state phase diagram consisting of the metallic state, the superconducting state, the phase separation, and insulating states at commensurate fillings. Compared to the homogeneous one-dimensional (1D) $t\text{\ensuremath{-}}J$ model, the superconductivity is greatly enhanced and stabilized by the flat-band structure. This superconducting state in periodically modulated chains shares similar properties with ladder systems: significant negative pair binding energy occurs, and the singlet-pairing correlation function dominates with the algebraic decay while the single-particle Green's function and spin correlation function decay exponentially. On the other hand, the superlattice structure leads to nontrivial topological nature in insulating states, characterized by different integer Chern numbers at different fillings. Due to the interplay among the topology, the interaction, and the 1D confinement, gapless edge modes show strong spin-charge separation and in different regions can relate to different collective modes, which are the charge of a single fermion, the magnon, and the singlet pair. We also find two interaction-driven topological transitions: (i) at particle filling $\ensuremath{\rho}=\frac{1}{2}$, the low-energy edge excitations change from the magnon to singlet pair, accompanied with pair formation in bulk; and (ii) at $\ensuremath{\rho}=\frac{3}{4}$, while the gapless edge mode is always the charge of a single fermion, there is a gap-closing point and a $\ensuremath{\pi}$-phase shift in the quasiparticle spectrum.