Competing density-wave orders in a one-dimensional hard-boson model

By P. Fendley, K. Sengupta, S. Sachdev. 2003

217 citations recorded by the source corpus.

We describe the zero-temperature phase diagram of a model of bosons, occupying sites of a linear chain, which obey a hard-exclusion constraint: any two nearest-neighbor sites may have at most one bosom. A special case of our model was recently proposed as a description of a "tilted" Mott insulator of atoms trapped in an optical lattice. Our quantum Hamiltonian is shown to generate the transfer matrix of Baxter's hard-square model. Aided by exact solutions of a number of special cases, and by numerical studies, we obtain a phase diagram containing states with long-range density-wave order with periods 2 and 3, and also a floating incommensurate phase. Critical theories for the various quantum phase transitions are presented. As a byproduct, we show how to compute the Luttinger parameter in integrable theories with hard-exclusion constraints.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/d673e18a8bffa28e0c88abd3ff143b6bf91a73bc

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Quantum Many-Body Scars: A Quasiparticle Perspective (2022, background): “(142), and, when ∆ = 0, is known as the PXP model.”
Provably efficient machine learning for quantum many-body problems (2021, unknown): “Our first example is a systemof trappedRydberg atoms (75, 76), a programmable and highly controlled platform for Ising-type quantum simulations (77–82).”
Observation of many-body scarring in a Bose-Hubbard quantum simulator (2022, methodology): “Finally, the effective Hamiltonian is equivalent to the PXP Hamiltonian ĤPXP = N∑ j=1 (P̂j−1σ̂+j P̂j+1 + P̂j−1σ̂−j P̂j+1) = N∑ j=1 P̂j−1X̂ j P̂j+1, (A4) when we set = −√2J and N = L − 1, with X̂ j ≡ |◦ j〉〈• j | + |• j〉〈◦ j | denoting the usual Pauli x matrix.”
Probing many-body dynamics on a 51-atom quantum simulator (2017, background): “Consistent with predictions from finite-size scaling analysis [30, 31], this peak is shifted towards positive values of ∆/Ω.”
Quantum many-body scars and weak breaking of ergodicity (2020, background): “[25] Paul Fendley, K.”