Entropy and entanglement in quantum ground states

By M. B. Hastings. 2007

167 citations recorded by the source corpus.

We consider the relationship between correlations and entanglement in gapped quantum systems, with application to matrix product state representations. We prove that there exist gapped one-dimensional local Hamiltonians such that the entropy is exponentially large in the correlation length, and we present strong evidence supporting a conjecture that there exist such systems with arbitrarily large entropy. However, we then show that, under an assumption on the density of states which is believed to be satisfied by many physical systems such as the fractional quantum Hall effect, that an efficient matrix product state representation of the ground state exists in any dimension. Finally, we comment on the implications for numerical simulation.

View Paper: https://www.semanticscholar.org/paper/327ba716bc5125c82085d61b00d137e8c5e62174

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Entanglement entropy and conformal field theory (2009, background): “Hastings [86] (see also [87]) provided a rigorous proof of the area law for one-dimensional systems with a generic local Hamiltonian, not necessarily close to a conformal critical point.”
The density matrix renormalization group in quantum chemistry. (2011, background): “F or p er so na l u se o nl y. –10 0 10 20 30 40 0 0.2 0.4 0.6 0.8 1 Re la ti ve e ne rg y (k ca l m ol –1 ) Isomerization coordinate CAS(16,14)-PT2 DMRG(28,32)-SC-CTSD DMRG(28,32)-SCF CR-CCSD(TQ)L RAS(24,28//4)PT2 Figure 6 Energies along an isomerization coordinate of Cu2O2.”
Exponential Decay of Correlations Implies Area Law (2012, background): “[31, 32] in order to ﬁnd a more explicit example of states in which exponential decay of correlations does not directly imply an area law.”
Computations in quantum tensor networks (2012, background): “Again, the underlying guideline is an area law [48, 18].”
Random matrix techniques in quantum information theory (2015, background): “lay other roles in quantum spin chain theory. In this section we follow [CGGPG13]. In the theory of quantum spin chains, it is nowadays widely well justied, both numerically [Whi92] and analytically [Has07], that ground states can be represented by the set of Matrix Product States with polynomial bo”
Superadditivity of communication capacity using entangled inputs (2009, methodology): “The map E is similar to that used[12] to construct random quantum expanders[13, 14], raising the possibility that deterministic expander constructions can provide stronger violations of additivity.”