Related papers: Higher Berry Connection for Matrix Product States
In this paper, we extend the quantum geometric tensor for parameter-dependent curved spaces to higher dimensions, and introduce an equivalent definition that generalizes the Zanardi, et al, formulation of the tensor. The parameter-dependent…
This paper reveals the intrinsic structure of Matrix Product States (MPS) by establishing their deep connection to entangled hidden Markov models (EHMMs). It is demonstrated that a significant class of MPS can be derived as the outcomes of…
In this paper, it is pointed out that the Berry's phase is a good index of degree of no-commutativity of the quantum statistical model. Intrinsic relations between the `complex structure' of the Hilbert space and Berry's phase is also…
Solving quantum many-body systems is one of the most significant regimes where quantum computing applies. Currently, as a hardware-friendly computational paradigms, variational algorithms are often used for finding the ground energy of…
A new approach extending the concept of geometric phases to adiabatic open quantum systems described by density matrices (mixed states) is proposed. This new approach is based on an analogy between open quantum systems and dissipative…
The many-body Berry phase formula for the macroscopic polarization is approximated by a sum of natural orbital geometric phases with fractional occupation numbers accounting for the dominant correlation effects. This reduced formula…
The Berry phase can be obtained by taking the continuous limit of a cyclic product $-\mbox{Im} \ln \prod_{I=0}^{M-1} \langle \Psi_0({\boldsymbol \xi}_I)|\Psi_0({\boldsymbol \xi}_{I+1})\rangle$, resulting in the circuit integral $i \oint…
It is known how to construct, in a bipartite quantum system, a unique low rank entangled mixed state with positive partial transpose (a PPT state) from an unextendible product basis (a UPB), defined as an unextendible set of orthogonal…
From topological viewpoint we have analysed the role of Berry phase in spin pairing mechanism of high $T_c$ superconducting state.
We present an adaptive variational quantum algorithm to estimate the Berry phase accumulated by a nondegenerate ground state under cyclic, adiabatic evolution of a time-dependent Hamiltonian. Our method leverages cyclic adiabatic evolution…
It is believed that most (perhaps all) gapped phases of matter can be described at long distances by Topological Quantum Field Theory (TQFT). On the other hand, it has been rigorously established that in 1+1d ground states of gapped…
As for a generic parameter dependent hamiltonian with the time reversal (TR) invariance, a non Abelian Berry connection with the Kramers (KR) degeneracy are introduced by using a quaternionic Berry connection. This quaternionic structure…
While general quantum many-body systems require exponential resources to be simulated on a classical computer, systems of non-interacting fermions can be simulated exactly using polynomially scaling resources. Such systems may be of…
Berry phase was originally defined for systems whose states are separated by finite energy gaps. One might naively expect that a system without a gap cannot have a Berry phase. Despite this we ask whether a Berry phase can be observed in a…
Topology describes properties of physical systems that remain constant under continuous deformations. For infinite vector waves, global topological invariants in position space are typically associated with periodic patterns. We demonstrate…
Lattice models consisting of high-dimensional local degrees of freedom without global particle-number conservation constitute an important problem class in the field of strongly correlated quantum many-body systems. For instance, they are…
Multipartite entanglement offers a powerful framework for understanding the complex collective phenomena in quantum many-body systems that are often beyond the description of conventional bipartite entanglement measures. Here, we propose a…
Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical…
Conical intersections are topologically protected crossings between the potential energy surfaces of a molecular Hamiltonian, known to play an important role in chemical processes such as photoisomerization and non-radiative relaxation.…
We show that for families of 1d lattice systems in an invertible phase, the cohomology class of the higher Berry curvature can be refined to an integral degree-3 class on the parameter space. Similarly, for families of U(1)-invariant 2d…