New class of exactly flat topological bands - compact localised states protected by local graph topology

• URL: http://arxiv.org/abs/2607.22831v1
• Date: Fri, 24 Jul 2026 18:14:36 GMT
• Title: New class of exactly flat topological bands - compact localised states protected by local graph topology
• Abstract summary: We introduce a prescription to construct an infinite family of exact flat band Hamiltonians supported on the faces of arbitrary graphs.<n>We prove that the extensive degeneracies of such face-graph Hamiltonians are protected by the local topology of the face-graph connectivity.<n>The resulting macroscopic null spaces yield compact localised states that remain localised over time due to frustration in hopping pathways.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Strongly correlated quantum matter is fundamentally defined by the tension between non-commuting quantum operators. Hamiltonians exhibiting macroscopic degeneracies are of general interest in this field because they imply an infinite susceptibility to any non-commuting perturbation. In moiré heterostructures, engineering such extensive degeneracies in the kinetic Hamiltonian creates a fertile garden for exotic strongly correlated phases of matter to emerge from the resulting flat bands. Here, we introduce a prescription to construct an infinite family of exact flat band Hamiltonians supported on the faces of arbitrary graphs. We demonstrate this algorithm on the faces of four Bravais lattices. Using a discrete graph generalization of the Atiyah-Singer index theorem, we prove that the extensive degeneracies of such face-graph Hamiltonians are protected by the local topology of the face-graph connectivity. The resulting macroscopic null spaces yield compact localised states that remain localised over time due to frustration in hopping pathways. We discuss the broad implications of such non-dispersing quantum modes in diverse settings, from arrested dynamics in quantum networks and quantum machine learning algorithms to Majorana-free topological quantum computation.

Related papers

• Quantum simulation of circular cluster interactions in a linear spin chain [41.99844472131922]
  Preparation of Hamiltonians with symmetries fundamentally different than those of the underlying device is a central challenge for quantum technologies.<n>We address this challenge with an analog protocol for the iconic generalized cluster Hamiltonian with the resultant translational symmetry from periodic boundary conditions.<n>Our results show that this goal can be achieved in a control duration that scales only moderately with the number of spins and Hamiltonian interaction complexity.
  arXiv  Detail & Related papers  (2026-08-25T12:48:48Z)
• Exact chiral symmetry with quantum signal processing [39.146761527401424]
  We give a quantum signal processing algorithm for the overlap fermion Hamiltonian.<n>Applying the overlap Hamiltonian costs only a factor logarithmic in $_e$ more than the Wilson-Dirac Hamiltonian.
  arXiv  Detail & Related papers  (2026-07-30T17:00:58Z)
• Topology from Decoherence [39.407739937584104]
  We show that decoherence can induce topological phenomena.<n>We demonstrate this in a lattice system subject to environment-induced dephasing.<n>Our results establish correlated quantum noise as a route to topology in open many-body systems.
  arXiv  Detail & Related papers  (2026-07-08T18:00:04Z)
• Hysteretic squashed entanglement in many-body quantum systems [42.085941481155295]
  Entanglement in many-body quantum systems is distributed across spatial regions.<n>We propose hysteretic entanglement $T_sq$, a conditional entanglement that measures the genuine quantum correlations between two subregions.<n>We show that $T_sq$ can detect genuine quantum correlations across both adjacent and long-range subsystems.
  arXiv  Detail & Related papers  (2026-03-10T17:00:49Z)
• Continuum field theory of matchgate tensor network ensembles [36.94429692322632]
  We develop a continuum description for random ensembles of two-dimensional fermionic matchgate tensor networks.<n>As a diagnostic of the resulting universal physics, we analyze disorder-averaged moments of fermionic two-point functions.<n>We show that disorder drives universal long-distance behavior governed by a nonlinear sigma-model of symmetry class D with a topological term.
  arXiv  Detail & Related papers  (2026-03-06T12:15:35Z)
• Bond Additivity and Persistent Geometric Imprints of Entanglement in Quantum Thermalization [4.588127679007806]
  We introduce a powerful framework, termed multi-bi partition entanglement tomography.<n>Our cornerstone is the discovery of a bond-additive law''<n>We apply this framework to Hamiltonian dynamics, random quantum circuits, and Floquet dynamics.
  arXiv  Detail & Related papers  (2026-01-04T01:59:52Z)
• Tomographic characterization of non-Hermitian Hamiltonians in reciprocal space [0.0]
  Non-Hermitian Hamiltonians enrich quantum physics by extending conventional phase diagrams.<n>We present an experimental photonic platform capable of simulating a non-unitary quantum walk generated by a peculiar type of non-Hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2025-12-10T17:57:27Z)
• Furthering Free-Fermion Findability From Fratricides [0.0]
  We present a novel graph-theoretic approach to simplifying generic many-body Hamiltonians.<n>Our approach expands the class of models that can be mapped to non-interacting fermionic Hamiltonians.<n>This framework provides new insights into Hamiltonian simplification techniques, free-fermion solutions, and group-theoretical characterizations relevant for quantum chemistry, condensed matter physics, and quantum computation.
  arXiv  Detail & Related papers  (2025-09-11T01:56:38Z)
• Robust analog quantum simulators by quantum error-detecting codes [22.034646136056804]
  We provide a recipe for error-resilient Hamiltonian simulations, making use of an excited encoding subspace stabilized by solely $2$-local commuting Hamiltonians.<n>Our method is scalable as it only requires penalty terms that scale to system size.
  arXiv  Detail & Related papers  (2024-12-10T18:58:05Z)
• Rigorous lower bound on dynamical exponents in gapless frustration-free systems [0.0]
  This work rigorously establishes a universal lower bound $zge2$ for the dynamical exponent in frustration-free quantum many-body systems.<n>Remarkably, our result can be applied to prove new bounds for dynamics of classical processes.
  arXiv  Detail & Related papers  (2024-06-10T16:08:33Z)
• Non-adiabatic holonomies as photonic quantum gates [36.136619420474766]
  We present the quantum-optical realization of non-adiabatic holonomies that can be used as single-qubit quantum gates. The inherent non-adiabaticity of the structures paves the way for unprecedented miniaturization.
  arXiv  Detail & Related papers  (2024-01-08T16:44:45Z)
• A simple approach to characterizing band topology in bosonic pairing Hamiltonians [0.0]
  We revisit the problem of characterizing band topology in dynamically-stable quadratic bosonic Hamiltonians that do not conserve particle number. We show this problem can be rigorously addressed by a smooth and local adiabatic mapping procedure to a particle number conserving Hamiltonian. Our approach shows that particle non-conserving bosonic Hamiltonians can be classified using known approaches for fermionic models.
  arXiv  Detail & Related papers  (2021-04-13T04:40:19Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• From communication complexity to an entanglement spread area law in the ground state of gapped local Hamiltonians [16.951941479979716]
  We make a connection between two seemingly different problems. The first problem involves characterizing the properties of entanglement in the ground state of gapped local Hamiltonians. The second problem is on the quantum communication complexity of testing bipartite states with EPR assistance.
  arXiv  Detail & Related papers  (2020-04-30T17:54:22Z)
• Quantum Geometric Confinement and Dynamical Transmission in Grushin Cylinder [68.8204255655161]
  We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder. We retrieve those distinguished extensions previously identified in the recent literature, namely the most confining and the most transmitting.
  arXiv  Detail & Related papers  (2020-03-16T11:37:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.