Two liquid states of distinguishable helium-4: The existence of another non-superfluid frozen by heating.

We show that two liquid states can exist in distinguishable helium-4 (4He) obeying Boltzmann statistics by path integral centroid molecular dynamics (CMD) simulations. This is an indication of quantum liquid polyamorphism induced by the nuclear quantum effect. For 0.08-3.3 K and 1-500 bar, we extensively conducted the isothermal-isobaric CMD simulations to explore not only possible states and state diagram but also the state characteristics. The distinguishable 4He below 25 bar does not freeze down to 0.1 K even though it includes no Bosonic exchange effect and, therefore, no Bose condensation. One liquid state, low quantum-dispersion liquid (LQDL), is nearly identical to normal liquid He-I of real 4He. The other is high quantum-dispersion liquid (HQDL) consisting of atoms with longer quantum wavelength. This is another non-superfluid existing below 0.5 K or the temperatures of LQDL. The HQDL is also a low-entropy and fragile liquid to exhibit, unlike conventional liquids, rather gas-like relaxation of velocity autocorrelation function, while there the atoms diffuse without noticeable contribution from quantum tunneling. The LQDL-HQDL transition is not a thermodynamic phase transition but a continuous crossover accompanied by the change in the expansion factor of quantum wavelength. Freezing of HQDL into the low quantum-dispersion amorphous solid occurs by heating from 0.2 to 0.3 K at 40-50 bar, while this P-T condition coincides with the Kim-Chan normal-supersolid phase boundary of real 4He. The obtained state diagram was compared to that of the confined subnano-scale 4He systems, where Bosonic correlation is considerably suppressed.