Related papers: Tangent-space methods for uniform matrix product s…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
Within the framework of relativistic quantum field theory, a novel method is established which allows to distinguish non-equilibrium states admitting locally a thermodynamic interpretation. The basic idea is to compare these states with…
Matrix Product State (MPS) wavefunctions have many applications in quantum information and condensed matter physics. One application is to represent states in the thermodynamic limit directly, using a small set of position independent…
Common wisdom says that the entanglement of fermionic systems can be low in the second quantization formalism but is extremely large in the first quantization. Hence Matrix Product State (MPS) methods based on moderate entanglement have…
Integrated gradients is prevalent within machine learning to address the black-box problem of neural networks. The explanations given by integrated gradients depend on a choice of base-point. The choice of base-point is not a priori obvious…
In this work, we prove that any element in the tensor product of separable infinite-dimensional Hilbert spaces can be expressed as a matrix product state (MPS) of possibly infinite bond dimension. The proof is based on the singular value…
We solve the mixing-demixing transition in repulsive one-dimensional bose-bose mixtures. This is done numerically by means of the continuous matrix product states variational ansatz. We show that the effective low-energy bosonization theory…
The tensor product representation of quantum states leads to a promising variational approach to study quantum phase and quantum phase transitions, especially topological ordered phases which are impossible to handle with conventional…
Improving the understanding of strongly correlated quantum many body systems such as gases of interacting atoms or electrons is one of the most important challenges in modern condensed matter physics, materials research and chemistry.…
Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…
The simulation of quantum systems is a task for which quantum computers are believed to give an exponential speedup as compared to classical ones. While ground states of one-dimensional systems can be efficiently approximated using Matrix…
The study of generic properties of quantum states has led to an abundance of insightful results. A meaningful set of states that can be efficiently prepared in experiments are ground states of gapped local Hamiltonians, which are well…
Matrix product states are useful representations for a large variety of naturally occurring quantum states. Studying their typical properties is important for understanding universal behavior, including quantum chaos and thermalization, as…
Entanglement entropy in topologically ordered matter phases has been computed extensively using various methods. In this paper, we study the entanglement entropy of topological phases in two-spaces from a new perspective---the perspective…
Any matrix product state $|\Psi\rangle$ has a set of associated kept and discarded spaces, needed for the description of $|\Psi\rangle$, and changes thereof, respectively. These induce a partition of the full Hilbert space of the system…
The contact geometric structure of the thermodynamic phase space is used to introduce a novel symplectic structure on the tangent bundle of the equilibrium space. Moreover, it turns out that the equilibrium space can be interpreted as a…
A central question in Quantum Computing is how matrices in $SU(2)$ can be approximated by products over a small set of generators. A topology will be defined on $SU(2)$ so as to introduce the notion of a covering exponent which compares the…
Curved spaces play a fundamental role in many areas of modern physics, from cosmological length scales to subatomic structures related to quantum information and quantum gravity. In tabletop experiments, negatively curved spaces can be…
In this note, we formulate and study a Hamilton-Jacobi approach for describing thermodynamic transformations. The thermodynamic phase space assumes the structure of a contact manifold with the points representing equilibrium states being…
We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework is reminiscent of state-sum models and lattice topological quantum field theories,…