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In this work, we aim to understand the effect of long-range hopping that decays with<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mi>r<\/mml:mi><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>&amp;#x2212;<\/mml:mo><mml:mi>&amp;#x03B1;<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:math>in non-Hermitian free-fermion systems. We first study two solvable Brownian models with long-range non-unitary dynamics: a large-<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>N<\/mml:mi><\/mml:math>SYK<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi\/><mml:mn>2<\/mml:mn><\/mml:msub><\/mml:math>chain and a single-flavor fermion chain and we show that they share the same phase diagram. When<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>&amp;#x03B1;<\/mml:mi><mml:mo>&amp;#x003E;<\/mml:mo><mml:mn>0.5<\/mml:mn><\/mml:math>, we observe two critical phases with subvolume entanglement scaling: (i)<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>&amp;#x03B1;<\/mml:mi><mml:mo>&amp;#x003E;<\/mml:mo><mml:mn>1.5<\/mml:mn><\/mml:math>, a logarithmic phase with dynamical exponent<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>z<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:math>and logarithmic subsystem entanglement, and (ii)<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>0.5<\/mml:mn><mml:mo>&amp;#x003C;<\/mml:mo><mml:mi>&amp;#x03B1;<\/mml:mi><mml:mo>&amp;#x003C;<\/mml:mo><mml:mn>1.5<\/mml:mn><\/mml:math>, a fractal phase with<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>z<\/mml:mi><mml:mo>=<\/mml:mo><mml:mfrac><mml:mrow><mml:mn>2<\/mml:mn><mml:mi>&amp;#x03B1;<\/mml:mi><mml:mo>&amp;#x2212;<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:mrow><mml:mn>2<\/mml:mn><\/mml:mfrac><\/mml:math>and subsystem entanglement<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>S<\/mml:mi><mml:mi>A<\/mml:mi><\/mml:msub><mml:mo>&amp;#x221D;<\/mml:mo><mml:msubsup><mml:mi>L<\/mml:mi><mml:mi>A<\/mml:mi><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mn>1<\/mml:mn><mml:mo>&amp;#x2212;<\/mml:mo><mml:mi>z<\/mml:mi><\/mml:mrow><\/mml:msubsup><\/mml:math>, where<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>L<\/mml:mi><mml:mi>A<\/mml:mi><\/mml:msub><\/mml:math>is the length of the subsystem<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>A<\/mml:mi><\/mml:math>. These two phases cannot be distinguished by the purification dynamics, in which the entropy always decays as<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>L<\/mml:mi><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>\/<\/mml:mo><\/mml:mrow><mml:mi>T<\/mml:mi><\/mml:math>. We then confirm that the results are also valid for the static SYK<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi\/><mml:mn>2<\/mml:mn><\/mml:msub><\/mml:math>chain, indicating the phase diagram is universal for general free-fermion systems. We also discuss phase diagrams in higher dimensions and the implication in measurement-induced phase transitions.<\/jats:p>","DOI":"10.22331\/q-2022-05-27-723","type":"journal-article","created":{"date-parts":[[2022,5,31]],"date-time":"2022-05-31T13:57:20Z","timestamp":1654005440000},"page":"723","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":39,"title":["Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics"],"prefix":"10.22331","volume":"6","author":[{"given":"Pengfei","family":"Zhang","sequence":"first","affiliation":[{"name":"Institute for Quantum Information and Matter and Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunxiao","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Physics, University of California Santa Barbara, Santa Barbara, CA 93106, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shao-Kai","family":"Jian","sequence":"additional","affiliation":[{"name":"Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, MD 20742, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Physics, Boston College, Chestnut Hill, MA 02467, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2022,5,27]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Xiangyu Cao, Antoine Tilloy, and Andrea De Luca. 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