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We show that the topological index of a wavefunction, computed in the space of twisted boundary phases, is preserved under Hilbert space truncation, provided the truncated state remains normalizable. If truncation affects the boundary condition of the resulting state, the invariant index may acquire a different physical interpretation. If the index is symmetry protected, the truncation should preserve the protecting symmetry. We discuss implications of this invariance using paradigmatic integer and fractional Chern insulators, $Z_2$ topological insulators, and Spin-$1$ AKLT and Heisenberg chains, as well as its relation with the notion of bulk entanglement. As a possible application, we propose a partial quantum tomography scheme from which the topological index of a generic multi-component wavefunction can be extracted by measuring only a small subset of wavefunction components, equivalent to the measurement of a bulk entanglement topological index.
Lattice translation symmetry gives rise to a large class of weak topological insulators (TIs), characterized by translation-protected gapless surface states and dislocation bound states. In this work we show that space group symmetries lead to constr
We study one-dimensional spin-1/2 models in which strict confinement of Ising domain walls leads to the fragmentation of Hilbert space into exponentially many disconnected subspaces. Whereas most previous works emphasize dipole moment conservation as
Although most quantum systems thermalize locally on short time scales independent of initial conditions, recent developments have shown this is not always the case. Lattice geometry and quantum mechanics can conspire to produce constrained quantum dy
Two-dimensional topological phases are characterized by TKNN integers, which classify Bloch energy bands or groups of Bloch bands. However, quantization does not survive thermal averaging or dephasing to mixed states. We show that using Uhlmanns para
We present an alternative scheme to the widely used method of representing the basis of one-band Hubbard model through the relation $I=I_{uparrow}+2^{M}I_{downarrow}$ given by H. Q. Lin and J. E. Gubernatis [Comput. Phys. 7, 400 (1993)], where $I_{up