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Register a new userIrreducible many-body correlations in topologically ordered systems
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Topologically ordered systems exhibit large-scale correlation in their ground states, which may be characterized by quantities such as topological entanglement entropy. We propose that the concept of irreducible many-body correlation, the correlation that cannot be implied by all local correlations, may also be used as a signature of topological order. In a topologically ordered system, we demonstrate that for a part of the system with holes, the reduced density matrix exhibits irreducible many-body correlation which becomes reducible when the holes are removed. The appearance of these irreducible correlations then represents a key feature of topological phase. We analyze the many-body correlation structures in the ground state of the toric code model in an external magnetic field, and show that the topological phase transition is signaled by the irreducible many-body correlations.
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While the interest in multipartite nonlocality has grown in recent years, its existence in large quantum systems is difficult to confirm experimentally. This is mostly due to the inadequacy of standard multipartite Bell inequalities to many-body systems: such inequalities usually rely on expectation values involving many parties and require an individual addressing of each party. In a recent work [J. Tura et al. Science 344, 6189 (2014)] some of us proposed simpler Bell inequalities overcoming such difficulties, opening the way for the detection of Bell correlations with trusted collective measurements through Bell correlation witnesses [R. Schmied et al. Science 352, 441 (2016)], hence demonstrating the presence of Bell correlations with assumptions on the statistics. Here, we address the question of assessing the number of particles sharing genuinely nonlocal correlations in a multipartite system. This endeavour is a priori challenging, as known Bell inequalities for genuine nonlocality suffer from the above shortcomings, plus a number of measurement settings scaling exponentially with the system size. We first show that most of these constraints drop once the witnesses corresponding to these inequalities are expressed: in systems where multipartite expectation values can be evaluated, these witnesses can reveal genuine nonlocality for an arbitrary number of particles with just two collective measurements. We then introduce a general framework focused on two-body Bell-like inequalities. We show that they also provide information about the number of particles that are genuinely nonlocal. Then, we characterize all such inequalities for a finite system size. We provide witnesses of Bell correlation depth $kleq6$ for any number of parties, within experimental reach. A violation for depth $6$ is achieved with existing data from an ensemble of 480 atoms.
We derive an exact lower bound to a universal measure of frustration in degenerate ground states of quantum many-body systems. The bound results in the sum of two contributions: entanglement and classical correlations arising from local measurements. We show that average frustration properties are completely determined by the behavior of the maximally mixed ground state. We identify sufficient conditions for a quantum spin system to saturate the bound, and for models with twofold degeneracy we prove that average and local frustration coincide.
Using Bell-inequalities as a tool to explore non-classical physical behaviours, in this paper we analyze what one can expect to find in many-body quantum physics. Concretely, framing the usual correlation scenarios as a concrete spin-lattice, we want to know whether or not it is possible to violate a Bell-inequality restricted to this scenario. Using clustering theorems, we are able to show that a large family of quantum many-body systems behave almost locally, violating Bell-inequalities (if so) only by a non-significant amount. We also provide examples, explain some of our assumptions via counter-examples and present all the proofs for our theorems. We hope the paper is self-contained.
We introduce a general bipartite-like representation and Schmidt decomposition of an arbitrary pure state of $N$ indistinguishable fermions, based on states of $M<N$ and $(N-M)$ fermions. It is directly connected with the reduced $M$- and $(N-M)$-body density matrices (DMs), which have the same spectrum in such states. The concept of $M$-body entanglement emerges naturally in this scenario, generalizing that of one-body entanglement. Rigorous majorization relations satisfied by the normalized $M$-body DM are then derived, which imply that the associated entropy will not increase, on average, under a class of operations which have these DMs as post-measurement states. Moreover, such entropy is an upper bound to the average bipartite entanglement entropy generated by a class of operations which map the original state to a bipartite state of $M$ and $N-M$ effectively distinguishable fermions. Analytic evaluation of the spectrum of $M$-body DMs in some strongly correlated fermionic states is also provided.
A hierarchy of equations for equilibrium reduced density matrices obtained earlier is used to consider systems of spinless bosons bound by forces of gravity alone. The systems are assumed to be at absolute zero of temperature under conditions of Bose condensation. In this case, a peculiar interplay of quantum effects and of very weak gravitational interaction between microparticles occurs. As a result, there can form spatially-bounded equilibrium structures macroscopic in size, both immobile and rotating. The size of a structure is inversely related to the number of particles in the structure. When the number of particles is relatively small the size can be enormous, whereas if this numbder equals Avogadros number the radius of the structure is about 30 cm in the case that the structure consists of hydrogen atoms. The rotating objects have the form of rings and exhibit superfluidity. An atmosphere that can be captured by tiny celestial bodies from the ambient medium is considered too. The thickness of the atmosphere decreases as its mass increases. If short-range intermolecular forces are taken into account, the results obtained hold for excited states whose lifetime can however be very long. The results of the paper can be utilized for explaining the first stage of formation of celestial bodies from interstellar and even intergalactic gases.
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