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      The density-matrix renormalization group

      Reviews of Modern Physics

      American Physical Society (APS)

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          Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms.

          For a system at a temperature of absolute zero, all thermal fluctuations are frozen out, while quantum fluctuations prevail. These microscopic quantum fluctuations can induce a macroscopic phase transition in the ground state of a many-body system when the relative strength of two competing energy terms is varied across a critical value. Here we observe such a quantum phase transition in a Bose-Einstein condensate with repulsive interactions, held in a three-dimensional optical lattice potential. As the potential depth of the lattice is increased, a transition is observed from a superfluid to a Mott insulator phase. In the superfluid phase, each atom is spread out over the entire lattice, with long-range phase coherence. But in the insulating phase, exact numbers of atoms are localized at individual lattice sites, with no phase coherence across the lattice; this phase is characterized by a gap in the excitation spectrum. We can induce reversible changes between the two ground states of the system.
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            Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

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              Density matrix formulation for quantum renormalization groups

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                Author and article information

                Journal
                RMPHAT
                Reviews of Modern Physics
                Rev. Mod. Phys.
                American Physical Society (APS)
                0034-6861
                1539-0756
                April 2005
                April 26 2005
                : 77
                : 1
                : 259-315
                10.1103/RevModPhys.77.259
                © 2005

                http://link.aps.org/licenses/aps-default-license

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