A proof of the Bloch theorem for lattice models
arXiv:1904.02700 · doi:10.1007/s10955-019-02386-1
Abstract
The Bloch theorem is a powerful theorem stating that the expectation value of the U(1) current operator averaged over the entire space vanishes in large quantum systems. The theorem applies to the ground state and to the thermal equilibrium at a finite temperature, irrespective of the details of the Hamiltonian as far as all terms in the Hamiltonian are finite ranged. In this work we present a simple yet rigorous proof for general lattice models. For large but finite systems, we find that both the discussion and the conclusion are sensitive to the boundary condition one assumes: under the periodic boundary condition, one can only prove that the current expectation value is inversely proportional to the linear dimension of the system, while the current expectation value completely vanishes before taking the thermodynamic limit when the open boundary condition is imposed. We also provide simple tight-binding models that clarify the limitation of the theorem in dimensions higher than one.
6 pages, 3 figures; v3: published version
References in corpus (3)
Cited by in corpus (28)
- Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
- Thermal transport, geometry, and anomalies
- Superconducting diode effect and nonreciprocal transition lines
- A many-body index for quantum charge transport
- Critical drag as a mechanism for resistivity
- On the general properties of non-linear optical conductivities
- Absence of energy currents in an equilibrium state and chiral anomalies
- Proximity-induced equilibrium supercurrent and perfect superconducting diode effect due to band asymmetry
- A Note on Bloch theorem
- Collisionless dynamics of general non-Fermi liquids from hydrodynamics of emergent conserved quantities
- Phase diagram of superconductivity in the integer quantum Hall regime
- Rigorous Index Theory for One-Dimensional Interacting Topological Insulators
- Microscopic formulas for thermoelectric transport coefficients in lattice systems
- Vanishing and non-vanishing persistent currents of various conserved quantities
- Chern-Simons-Matter Theories at Large Baryon Number
- Higher-dimensional generalizations of the Thouless charge pump
- On the absence of stationary currents
- Nernst and Ettingshausen effects in gapped quantum materials
- Spin loop-current textures in Hubbard models
- Motion from Measurement: The Role of Symmetry of Quantum Measurements
- Drude weights in one-dimensional systems with a single defect
- Vortical effects in chiral band structures
- Equality of magnetization and edge current for interacting lattice fermions at positive temperature
- Dirac bilinears in condensed matter physics: Relativistic correction for observables and conjugate electromagnetic fields
- Majorana Flat Bands in the Vortex Line of Superconducting Weyl Semimetals
- Hopf symmetry protected topological phases in the vicinity of spin orders
- The Bloch theorem in the presence of an additional conserved charge
- Persistent current-carrying state of charge quasuparticles in -ribbon featuring single Dirac cone