Area-law and universality in the statistics of the subsystem energy

Talk

Consider a quantum chain in its ground state and then take a subdomain of this system with natural truncated hamiltonian. Since the total hamiltonian does not commute with the truncated hamiltonian the subsystem can be in one of its eigenenergies with different probabilities. Since the global energy eigenstates are locally close to diagonal in the local energy eigenbasis we argue that the Renyi entropy of these probabilities follows an area-law for the gapped systems. When the system is at the critical point the Renyi entropy follows a logarithmic behaviour with a universal coefficient which is proportional to the central charge. Our results show that the Renyi entropy of the subsystem energies closely mimics the behaviour of the entanglement entropy in the quantum chains. We also connect our problem to the Loschmidt echo setup which may help to measure the generating function of our probabilities using the current technologies. Since the introduced probabilities follow closely the Schmidt coefficients our protocol can be used to measure the Schmidt coefficients effectively.

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