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Many-Body Bound States in the Continuum (2307.05456v1)

Published 11 Jul 2023 in quant-ph, cond-mat.quant-gas, and cond-mat.stat-mech

Abstract: A bound state in the continuum (BIC) is a spatially bounded energy eigenstate lying in a continuous spectrum of extended eigenstates. While various types of single-particle BICs have been found in the literature, whether or not BICs can exist in genuinely many-body systems remains inconclusive. Here, we provide numerical and analytical pieces of evidence for the existence of many-body BICs in a one-dimensional Bose-Hubbard chain with an attractive impurity potential, which was previously known to host a BIC in the two-particle sector. We also demonstrate that the many-body BICs prevent the system from thermalization when one starts from simple initial states that can be prepared experimentally.

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  48. (b), An example of such an operator A^xsubscript^𝐴𝑥\hat{A}_{x}over^ start_ARG italic_A end_ARG start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT is A^x=2⁢cos⁡(π4⁢n^x)⁢cos⁡(π4⁢(n^x+1))(n^x+2)⁢(n^x+1)⁢b^x2,subscript^𝐴𝑥2𝜋4subscript^𝑛𝑥𝜋4subscript^𝑛𝑥1subscript^𝑛𝑥2subscript^𝑛𝑥1superscriptsubscript^𝑏𝑥2\displaystyle\hat{A}_{x}=\sqrt{\frac{\sqrt{2}\cos\quantity(\frac{\pi}{4}\hat{n% }_{x})\cos\quantity(\frac{\pi}{4}(\hat{n}_{x}+1))}{(\hat{n}_{x}+2)(\hat{n}_{x}% +1)}}\ \hat{b}_{x}^{2},over^ start_ARG italic_A end_ARG start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT = square-root start_ARG divide start_ARG square-root start_ARG 2 end_ARG roman_cos ( start_ARG divide start_ARG italic_π end_ARG start_ARG 4 end_ARG over^ start_ARG italic_n end_ARG start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT end_ARG ) roman_cos ( start_ARG divide start_ARG italic_π end_ARG start_ARG 4 end_ARG ( over^ start_ARG italic_n end_ARG start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT + 1 ) end_ARG ) end_ARG start_ARG ( over^ start_ARG italic_n end_ARG start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT + 2 ) ( over^ start_ARG italic_n end_ARG start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT + 1 ) end_ARG end_ARG over^ start_ARG italic_b end_ARG start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT , (15) where n^x≔b^x†⁢b^x≔subscript^𝑛𝑥superscriptsubscript^𝑏𝑥†subscript^𝑏𝑥\hat{n}_{x}\coloneqq\hat{b}_{x}^{\dagger}\hat{b}_{x}over^ start_ARG italic_n end_ARG start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT ≔ over^ start_ARG italic_b end_ARG start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT start_POSTSUPERSCRIPT † end_POSTSUPERSCRIPT over^ start_ARG italic_b end_ARG start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT .
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